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From YouTube: IETF104-QIRG-20190325-1610
Description
QIRG meeting session at IETF104
2019/03/25 1610
https://datatracker.ietf.org/meeting/104/proceedings/
A
B
Right
it's
4:10
p.m.
so.
If
you
all
would
take
your
seats,
are
you
ready
Ben?
Let's
do
it
welcome
to
the
quantum
Internet
research
group
meeting
here
in
Prague,
and
today
we
have
two
hours.
As
you
know,
this
session
is
a
tutorial
session.
I'm
rod
van
Meter
I
am
one
of
the
Working
Group
co-chairs.
My
co-chair
Stephanie
Vayner
is
not
here
today,
but
we
have
with
us
Tracy
Northup
from
Innsbruck
who's,
going
to
help
me
with
the
the
tutorial.
B
So
we'll
do
that
for
a
couple
of
hours
today,
we're
gonna
try
to
take
about
a
five
minute
break
just
to
give
everybody
time
to
stretch
their
legs
about
half
way.
Throat
and
also
this
session
is
the
tutorial
tomorrow
will
be
the
working
group
meeting
where
we're
going
through
the
existing
set
of
drafts
and
what
not
compute
next
pitch.
So
yes,
as
you
know,
we
are
in
the
Grand
Ballroom
for
those
of
you
who
are
online
or
if
you
need
the
URLs
there's
the
there's.
B
The
connection
next
page
and
tomorrow
will
be
1120,
will
be
downstairs
in
congress
hall
for
the
for
the
working
group
meeting
there
and
we'll
cover
the
active
set
of
internet
drafts,
of
which
there
are
about
three,
although
they're
not
all
correctly
tracked
in
the
system.
Yet
there
are
at
least
three
that
are
relevant
to
what
we're
doing
and
a
couple
of
other
things
and
next
page.
So
the
history
and
status
of
this
group
just
very
very
quickly
for
those
of
you
who
are
in
the
room
for
the
first
time
we're
hearing
about
this.
B
B
We
opened
the
mailing
list
after
that,
and
we
were
approved
tentatively
as
a
proposed
research
group
in
November
and
met
in
Bangkok,
where
we
had
an
overflow
room,
120
or
so
people
I
think
we're
on
the
blue
sheets
and
our
proposed
plan,
which
we
may
or
may
not
stick
to
in
its
entirety,
is
to
meet
once
a
year
here
at
IETF
and
once
a
year
at
a
quantum
conference,
and
once
a
year,
virtually
online,
just
sort
of
roughly
okay
looks
like
so
today.
Let's
see
we
have
the
blue
sheets
going
at
around.
B
We
have
a
note
taker
and
a
gem
jabber
scribe
already
taken
care
of,
so
we're
in
good
form,
good
shape
there
and
tutorial
wise.
Although
the
agenda
says
first
half
me
and
architectural
concepts
and
second
half
Traci
and
implementations,
we're
actually
going
to
sort
of
switch
back
and
forth
a
little
bit
as
we
go.
Instead,
it's
going
to
be
a
little
bit
more
mixed
and
we
would
like
to
make
this
as
interactive
as
possible.
B
So,
if
there's
anything
along
the
way
that
you
have
a
question
about,
feel
free
to
step
to
the
mic
and
ask
your
we'll
recognize
you
that
sort
of
a
reasonable
stopping
point
and
consistent
with
forward
progress
will
take
as
many
questions
as
we
can
during
the
course
of
this.
Let's
go
ahead
and
switch
to
the
other,
the
other
laptop
yeah,
any
comments
or
questions
on
what
we're
doing
before
we
get
started.
B
We
have
presentation
good,
all
right,
so
rough
outline
of
what
we're
gonna
talk
about.
I'm
gonna.
Give
you
a
few
minutes
on
the
teat
aldea.
A
tldr
version
of
what
a
quantum
network
is
spend
some
time
talking
about
what
applications
we
might
run
on
it,
which
should
be
kind
of
why
you
care
some
basic
concepts
and
terminology,
and
some
math
and
whatnot
and
then
somewhere
down
in
through
here.
B
Roughly,
there
are
two
kinds
of
quantum
networks:
there
are
unentangled
networks
which
are
good
for
primarily
for
quantum
key
distribution,
which
is
essentially
making
shared
secret
bits
across
a
network
where
the
secrecy
of
those
bits
is
guaranteed
via
the
underlying
physics,
rather
than
some
sort
of
mathematical
function
and
the
these
networks
exist.
They
are
limited
in
distance
and
their
single
purpose,
and
they
have
other
constraints
which
some
of
you
all
are
aware
of,
but
did
you
exist
at
the
other
end
of
the
spectrum
lie
entangled
network
good
for
many
different
purposes.
B
Cryptographic
functions,
high-precision
networks
connecting
quantum
computers
into
a
real
quantum
Internet
and
covering
long
distances
and
whatnot,
and
these
things
are
particularly
difficult
to
build,
but
Tracy
and
other
people
are
working
on
that
and
in
between
these
two
major
categories
of
networks.
There's
a
series
of
steps,
I'm
defined
by
stephanie
and
her
collaborators
and
we'll
show
you
just
a
little
bit
more
about
that
as
we
go
axel.
Also
axel
Dahlberg
from
from
Stephanie's
group
presented
some
of
this
in
bangkok,
with
it,
with
a
really
good
overview
of
that
right.
B
If
you
measure
the
one
on
the
left
to
figure
out
what
it
looks
like
what
it's
actually
doing,
it
will
be,
you
will
find
that
it's
either
pointed
up
or
pointed
down,
and
in
this
case
it
was
pointed
down.
At
the
same
time,
you
will
learn
what
the
one
at
the
far
end
is,
even
if
these
two
systems
were
far
apart.
This
is
sort
of
the
basic
idea
of
entanglement
that.
C
B
So
the
job
of
a
quantum
repeater
network
is
to
make
this
entanglement
end-to-end
between
pair
of
notes,
modulo,
some
arguments
we're
not
going
to
get
into
it
get
into
about
the
ordering
of
events
and
whatnot
and
importantly,
entanglement,
is
a
consumable
resource,
and
so
we
have
to
make
lots
and
lots
of
it
as
we
go.
That's
the
job
of
the
quantum
network
is
to
regenerate
this
entanglement
sort
of
continuously.
B
Third
to
monitor
and
manage
errors,
as
it
goes,
we'll
look
at
a
couple
of
techniques,
one
of
the
ones
we'll
talk
about
the
most
is
what's
called
purification.
There's
also.
Quantum
error.
Correction
and
fourth
is
to
participate
in
the
management
of
the
network
itself,
so
routing
protocols
and
security
and
path,
setup
and
teardown
and
multiplexing,
and
all
those
other
sorts
of
things
that
the
people
in
this
room
know
better
than
anybody.
B
So
if
that's
the
job
of
a
quantum
repeater,
then
or
and
and
an
individual
network,
then
the
job
of
a
quantum
Internet,
as
opposed
to
a
quantum
network,
is
to
do
all
of
this
across
heterogeneous
networks,
both
physically
and
logically,
in
an
environment
with
minimal
trust
between
those
networks.
And
that
includes
having
no
knowledge
of
the
internals
of
the
autonomous
networks,
the
equivalent
of
the
Internet's
autonomous
systems
and
possibly
in
the
presence
of
malicious
notes.
B
These
are
the
kinds
of
areas
where
the
quantum
physicists,
not
only
I'm,
going
to
say
this,
even
though
in
front
of
a
physicist,
even
though
Tracy's
here
on
the
the
physicists,
not
only
don't
know
a
lot
of
these
things
in
a
lot
of
cases,
they
don't
know
what
they
don't
know,
but
there's
an
awful
lot
of
problems
that
have
to
be
solved
from
going
from
having
a
physical
layer
in
a
network
up
through
layers
to
through
nine
or,
however
many
layers
you
want
to
have.
So
that's
the
alright
going
on.
B
So
they,
however,
make
how
many
protocol
layers
you
happen
to
care
to
have
so.
The
job
of
the
people
in
this
room
is
to
help
guide
those
experimentalists
who
are
building
those
networks
and
help
us
to
build
complete
systems.
The
same
same
as
was
done
with
radio
and
fiber
and
everything
else,
as
we
went
over
the
course,
the
last
50
years
several
years
ago.
Let's
see
how
long
was
it's
now?
Do
you
remember
when
this
paper
was.
D
B
I
think
the
group
of
Leon
Jung
from
Yale
University
to
find
a
set
of
generations
of
networks
they
defined
what
they
called
1g
2g
3G
networks
and
we're
going
to
talk
a
little
bit
more
about
what
those
different
kinds
of
network
of
networks
actually
are
and
represent.
You'll
notice
that
on
the
left,
they
describe
two
classes
of
errors,
there's
loss,
error,
meaning
Lee
or
the
loss
of
your
individual
photons
as
they're
going
down
a
fiber
and
then
there's
operational
error
noise
in
the
system,
decay
of
your
memory
and
whatnot.
B
So
the
loss
error
obviously
operates
at
the
link
layer
and
the
operational
layer
you
have
or
the
operations
errors
we
have
to
deal
with
at
the
end,
to
end
layer,
there's
a
whole
bunch
of
stuff
that
has
to
be
done.
We
have
to
you
can't
deal
with
this
simply
hop
by
hop
and
we'll
we'll
explain
how
that
is.
Is
we
go?
B
B
They
think
maybe
we'll
either
be
able
to
violate
the
speed
of
light
and
transmit
information
faster
than
the
speed
of
light
I'm
here
to
disappoint
you
and
tell
you,
that's
not
the
case,
and
it's
also
not
the
case
that
quantum
networks
are
going
to
be
some
some
pathway
to
care
a
bit
X
a
bit
yot
a
bit
per
second
kinds
of
networks.
That's
that's!
Not
what
we're
trying
to
do
here.
B
We're
gonna,
bring
in
new
kinds
of
capabilities
into
the
networks,
improvements
in
the
number
of
communication
rounds
for
certain
distributed
protocols,
higher
precision,
scalability
of
distributed
systems
and
whatnot
all
right,
so
going
a
little
bit
more
into
the
the
applications
themselves.
I
divide
the
set
of
applications
that
we
can
do
with
a
quantum
Internet
into
three
large
areas.
B
The
sensor
networks
are
high,
very
high
bandwidth
and
the
distributed
computation
is
also
high,
very
high
bandwidth.
So
certainly
in
the
short
run,
the
crypto
functions
are
going
to
be
the
thing
that's
going
to
be
adoption,
the
others
are
gonna,
take
a
little
bit
more
time
to
get
there.
But
let
me
go
through
an
example
with
each
one
of
these
categories
and
show
you
the
kinds
of
things
we
want
to
do.
This
particular
one
goes
back
to
a
an
internet
draft
that
Sholto
nagahama
sitting
over
there
and
I
wrote
back
in
2014.
B
B
We
can
have
all
sorts
of
discussions
about
that.
But
that's
the
idea
right
and
those
keys
are
exchanged
with
the
IPSec
gateways
in
some
particular
in
some
secure
fashion
and
then
they're
actually
used
to
encrypt
data.
That's
transmitted
across
the
IP
network.
So
that's
the
basic
structure.
This
could
also
be
applied
to
TLS,
Sheila
Franco
I
think
was
someone
who
proposed
this.
We
actually
did
a
little
bit
of
analysis
on
it.
B
Obviously,
at
the
client
end
you're
going
to
need
a
single
connection
and
at
the
server
end
you're
going
to
need
many
connections
and
for
the
the
clients
connection
you
need
to
be
able
to
generate
maybe
a
hundred
bits
per
second
or
something
and
at
the
server
end
you're
going
to
need
megabits
on
on
up
and
performance
of
this.
So
the
IPSec
use
case
is
pretty
symmetric,
whereas
the
the
TLS
case
has
concentrated
your
same
as
network
architectures
right.
B
Someone
may
find
some
vulnerability
in
a
yes
something
we
don't
suspect
it
actually
exists
today
and
then,
maybe
in
some
sort
of
hypothetical
strongman,
maybe
it's
possible
to
test
all
of
the
keys
all
of
the
possible
key
combinations.
So
if
your
encrypted
data
today,
the
data
is
secure
from
now
until
someone
factors
a
number
if
they
have
recorded
your
your
encrypted
conversation
today,
that's
being
sent
across
the
network
and
then
in
ten
years
this
factoring
becomes
possible.
Then
they
can
decrypt
the
conversation
you're
having
today
ten
years
from
now
with
Q
KD
+
AES.
B
So
the
question
is:
is
the
gap
between
these
two
states
of
future
history
actually
interesting
the
gap
between
when
factoring
becomes
possible
and
when
a
EES
gets
broken?
If
so,
you
should
be
looking
at
employ
deploying
that
qkd
today,
by
the
way,
if
you
haven't
seen
the
website,
we
tweaked
th
org.
If
you
are
a
particular
cryptographer,
I
would
love
to
have
the
opinion
of
people
on
that
particular
approach
today.
B
If
you
want
to
do
this,
qkd
plus
a
yes
you're
gonna
need
data
rates
on
the
order
of
bits
per
second,
in
order
to
roll
your
keys
over
and
sort
of
reasonable
time
with
super
8.
Yes,
it's
going
to
be
the
same,
whereas
with
one
time
pad,
obviously
you're
going
to
need
to
be
able
to
reach
up
toward
billions
of
bits
per
second
in
order
to
do
this
sort
of
reasonably
so,
as
you
can
see,
we've
got
sort
of
nine
orders
of
magnitude.
B
A
performance
range
there,
as
performance
improves,
new
capabilities
will
come
on
light,
it'll
become
possible
to
do
new
things
right.
So
that's
the
crypto
use
case
the
crypto
scenario,
from
the
big
bubble
that
I
had
in
the
three
bubbles.
Let's
talk
about
distributed
computing,
there's
a
concept
known
as
blind
computation,
which
is
secure
quantum
time
sharing,
give
or
take
I'm
sure
many
of
you
recognize
that
deck
system
10
up
there.
Some
of
you
may
have
actually
programmed
it.
The
original
ARPANET
vision
was
taking
a
system
like
that
and
a
network
that
looked
like
this.
B
This
little
map,
or
a
a
copy
thereof,
still
hung
on
the
wall
at
ISI.
When
I
arrived
at
isi
in
1986.
Oh,
this
is
the
1973
version
of
it.
This
is
your
ARPANET,
and
then
you
have
some
small
system
in
front
that
behaves
as
a
front-end
and
we're
going
we're
going
to
connect
our
small
quantum
computer
at
our
house
or
laboratory
and
connect
it
to
a
mainframe
across
the
quantum
internet
and
everything's
gonna
be
hunky-dory
right.
All
this
is
going
to
be
cool.
B
Well,
that's
not
bad
right,
so
bad,
but
why
is
that
different
from
what
we
can
do
today?
We're
literally,
my
group
in
Japan
right
now,
is
literally
connecting
via
the
existing
Internet
to
IBM's
Research
Center
in
Yorktown
Heights
and
using
their
quantum
computers
that
are
in
a
laboratory
in
New
York
remotely
from
from
Japan.
So
right
we
can
already
do
that
right.
So
what
do
we
need?
A
quantum
internet,
for
we
can
already
build
distributed
systems
like
that.
B
Well,
what
you
get
by
being
able
to
do
this
in
a
distributed
fashion
and
doing
this
using
a
quantum
Internet
and
this
blind
computation
is.
It
allows
us
to
execute
a
computation
on
the
server
in
which
the
server
learns
nothing
about
the
clients
data,
either
the
input
or
the
output,
nor
even
the
computation,
except
some
sort
of
upper
bound
on
the
size
of
the
computation
itself.
So
in
that
sense,
it's
actually
even
stronger
than
the
classical
version
of
the
classical
homomorphic
encryption.
If
you're
familiar
with
that,
so
I
really
love
this.
B
This
is
I
think,
ultimately,
one
of
the
driving
reasons
to
build
a
quantum
Internet,
and
it's
also
then
open
up
a
whole
lot
of
interesting
applications
across
a
variety
of
things,
and
this
has
actually
even
been
demonstrated
in
the
laboratory
at
sort
of
the
one
qubit
level
we're
not
talking
about
some
giant
computation
but
doing
it
via
some
analysis.
We've
actually
found
that
it's
going
to
take
very
high
data
band
or
data
rates
in
order
to
execute
this
for
large
computation,
it's
maybe
10
to
the
10
somewhere
around
there.
B
The
third
scenario
that
I
mentioned
was
sensor
networks,
so
I
sort
of
defined
sensor
networks
sort
of
broadly.
There
are
algorithms
that
have
defined
for
doing
high-precision
clock
synchronization.
There
are
algorithms
for
doing
high-precision
position
finding
and
in
this
particular
case
there
are
also
algorithms
for
taking
distributed
quantum
states
and
using
them,
as
essentially
a
phase
reference
in
astronomical
interferometry,
which
allows
you
to
get
higher
resolution
images
than
couldn't
be
done
using
the
existing
interferometry.
B
That's
done
between
antennas,
like
there's
a
couple
of
antennas
in
this
picture,
so
this
looks
this
looks
really
great
too
right.
In
theory.
We
can
use
this,
for
you
know
sorts
of
cyber-physical
uses
and
improving
different
kinds
of
sensor
networks
as
we
go.
Sadly,
this
was
also
an
even
higher
bandwidth.
B
This
is
probably
going
to
take
something
like
10
to
the
11
operations
per
second
or
bits
per
second
entanglements
per
second,
in
order
to
do
this
or
usefully-
and
finally,
this
is
an
area
I
actually
haven't
spent
much
time
looking
at,
because
I'm
not
I'm,
not
sure
it's
actually
practical,
but
there
are
a
number
of
research
papers
out
there
that
are
showing
that,
given
the
existence
of
entanglement,
we
can
actually
get
exponential
reduction
in
the
number
of
rounds.
You
need
to
solve
particular
problems.
B
You
know
exponential
as
the
size
of
your
network
grows,
so
there's
a
set
of
things
that
are
out
there
potentially
worth
taking
a
look
at
at
some
point
technical
demands.
Some
of
these
require
only
the
ability
to
actually
measure
Q
of
photons
that
come
at
you,
so
you're
sitting
at
home.
You
don't
necessarily
have
to
have
a
complete
quantum
computer
at
home,
but
you've
got
a
pipe
coming
in.
You've
got
a
fiber
or
something
coming
in,
and
individual
photons
are
coming
out
of
that
fiber.
B
You
need
the
ability
to
measure
those
that's
at
one
end
of
the
technical
spectrum.
The
other
end
of
the
technical
spectrum
is
runs
all
the
way
from
all
the
way
up
to
having
really
high
precision
quantum
memories
and
a
large-scale
quantum
computer
at
your
node.
In
order
to
actually
execute
interesting
algorithms
over
that
and
that's
sort
of
a
relatively
long
way
away.
This
is
on
the
lower
left.
There
is
a
series
of
stages,
but
the
evolution.
These
networks
will
go
through
again.
B
That's
from
the
roadmap
that
was
actually
developed
by
a
Stephanie
Boehner
and
her
team.
Any
questions
on
applications.
Now
it
might
be
a
reasonable
time
to
ask
for
that
for
the
first
round
of
questions
I've
been
talking
for
about
20
minutes
now,
20
minutes.
Yes,
questions
I
can't
possibly
have
convinced
everyone
that
all
of
this
is
entirely
practical,
which
means
that
if
there
are
no
questions
that
none
of
you
have
understood
any
of
it
right,
I,
don't
believe
either
of
those
things
to
be
true.
So
I'm
sure
someone
here
has
a
question.
E
B
Note,
which
I
should
have
said
and
emphasized
repeatedly,
while
up
here
at
the
front
so
to
speak,
yeah
is
that
quantum
repeaters
are
not
the
same
thing
as
classical
repeaters.
Don't
blame
me:
don't
blame
Tracy
blame
whoever
was
the
wrote
the
first
paper
on
these
things
about
20
years
ago
and
called
them
repeaters.
They
are
not
like
classical
repeaters.
They
are
not
so
amplifiers.
B
They
are
nodes
that
are
actually
active
devices
during
a
particular
set
of
operations
that
are
used
to
help
us
extend
entanglement
across
multiple
hops
and
we're
gonna
get
into
the
architecture
that
stuff
for
the
next
hour.
So
good
question,
though,
thank
you
for
bringing
that
up,
since
that
was
a
good
technical
point.
Yes,.
D
I
think
that
might
be
referring
to
the
sense
of
you
know
if
you
can
create
a
quantum
state
as
a
resource
to
use
for
your
computation,
then
yeah
at
that
point
it
doesn't
matter
to
us
how
far
apart
it
is,
but
it's
in
order
to
create
those
quantum
states
over
long
distances
that
we
then
need
repeaters.
So
it's
in
the
repeaters
are
kind
of
for
the
creation
of
quantum
states,
as
resources
and
I.
Think
we'll
get
more
to
the
details
of
that
coming
up.
Does
that
help.
F
B
At
the
moment,
so
my
team
in
in
Japan
is
using
a
20
qubit
superconducting
computer
that'sthat's
in
a
laboratory
in
Yorktown
I
was
chatting
with
my
team.
You
know,
via
slack
just
right
before
we
started
this
and
they're
actually
doing
some
stuff
right
now,
but
those
existing
machines,
the
20
cubed
systems,
are
good
enough
to
start
testing
stuff
and
start
running
very,
very
tiny
algorithms
on
top
of
them,
but
nothing
not
like
anything
that
you
would
really
recognize
as
sort
of
a
reasonable
computation.
It's
still
pretty
much
at
the
test
stage.
B
My
group
is
working
on
compiler
technology,
so
we're
trying
to
figure
out
how
to
optimize
programs
that
are
written
by
a
by
a
programmer
in
a
python-based
toolkit
called
kis
get.
This
is
the
kiss
kid
t-shirt.
If
you
use
kiss
kit
you
can
you
can
kiss
kit
has
functions
built-in
for
for
logging
into
the
remote
system.
B
Excuse
me
and
sending
your
program
from
your
laptop
to
their
controllers
over
there,
and
then
they
execute
it
10,000
times
over
there,
and
then
they
give
you
back
statistical
data,
there's
no
real,
interactive
control.
It's
very
much
batch
stuff
that
you
can
do
and
the
sets
of
things
that
you
can
do
with
it
there.
There
are
a
handful
of
very
small
algorithms
that
you
can
run
on
that
and
then
sort
of
squint
and
say
yeah.
The
data
kind
of
looks
like
what
it
was
supposed
to,
but
they're
getting
better
rapidly.
B
B
Some
of
them
are
available
for
free
on
IBM
has
1/5
qubit
computer
and
114
qubit
computer,
that
anybody
can
go
log
in
log
in
on
and
create
an
account
and
run
things
remotely
from
here
so
to
Righetti
and
google
and
other
people
well,
some
of
those
aren't
I,
don't
think
actually
public
yet,
but
and
Tracy's
group
in
in
Innsbruck
is
actually
building
computers
on
a
on
a
different
technology
known
as
ion
traps.
So
there's
a
bunch
of
stuff:
that's
out
there,
it's
still
early,
but
there's
a
lot
of
progress.
Being
made
any
comments.
D
D
G
B
Hillman,
yes,
so
that's
replaced
iffy
Hellman,
with
with
with
the
quantum
key
distribution
on
some
of
the
products,
I'm
not
familiar
with
the
details
of
all
of
them,
but
I
know
in
at
least
one
case.
What
they're
actually
doing
is
they're
actually
running
two
layers
of
encryption
and
they're
running
one,
your
bulk
and
encryption,
using
keys
generated
via
standard
diffie-hellman
and
another
layer
using
keys
generated
by
qkd,
and
you
can
either
view
that
as
a
way
to
mollify
people
who
don't
believe
in
qkd
or
view
it
as
they
don't
have
faith
in
their
own
device.
B
Sue
just
I
saw
you
moving.
That
way.
Does
that
mean
there
was
a
question
by
a
jabber
or
something
no
okay,
time
wise.
We
should
move
on
so
some
basic
terminology
and
questions
or
concepts.
1
2,
3,
4,
5,
6,
7
concepts,
I'm
not
going
to
go
through
all
of
these
in
detail.
These
are
sort
of
vocabulary
for
you
for
you
to
a
vocabulary,
homework
for
you
to
take
home
and
look
at
you'll
you'll
get
a
few
of
these.
B
As
we
go
a
few
terms
we
will
actually
use
in
the
course
of
this
quantum
amplitude
means
the
amount
of
your
total
quantum
probability
wave
function,
thingamabob,
that
is
in
a
particular
state,
and
it's
represented
by
a
complex
number.
A
pure
state
means
a
quantum
state
where
your
hardware
actually
worked.
The
way
it
was
supposed
to.
It
actually
did
what
it
was
supposed
to
do,
and
we
described
that
as
having
a
fidelity
of
1.0.
B
A
mixed
state
is
one
that
has
noise
and
errors
in
it
and
has
fidelity
less
than
1.0,
so
mixed
state,
some
people
talk
about
and
we'll
get
into
superposition
and
entanglement,
and
things
like
that.
People
from
sort
of
outside
the
field
occasionally
use
the
term
mixed
state
when
they,
when
they're
talking
about
those
things,
don't
get
confused
mixed
state
means
means
your
hardware
sucks
right.
B
B
We've
all
seen
waves,
you've
seen
another
wave
like
this
to
it
with
slightly
different
frequencies.
You
add
them
up
and
you
get
something
that
looks
like
that
right.
This
is
normal
waves
at
the
moment.
We're
not
doing
anything
at
all
quantum,
but
this
gets
you
what
you
call
interference
so
over
here
at
the
left,
where
your
two
waves
are
in
phase,
they
add
up
and
you
get
what's
called
constructive
interference
and
they're
in
the
middle,
where
the
way
it's
are
out
of
phase
they
cancel
out
and
you
get
what's
called
destructive
interference.
B
This
happens
at
the
quantum
level
with
individual
photons
and
individual
electrons
and
whatnot.
That's
one
of
the
key
concepts
that
that's
actually
required
to
understand:
quantum
computing,
all
right.
So
a
couple
of
things
about
the
basic
mathematical
notation
dude
named
Dirac,
who
is
one
of
the
the
people
who
helped
create
quantum
mechanics
to
find?
B
What's
called
the
bra,
ket
notation
you'll
see
there
a
couple
of
examples
or
three
examples
of
two-dimensional
vectors
and
what
we
do
is
we
write
this
like
this
using
this
funny
vertical
pipe
and
an
angle
bracket,
that's
our
what
would
call
our
zero
state
so
that
vector
is
defined
to
be
the
zero
state.
This
vector
is
defined
to
be
the
one
state
and
if
you
put
them
together,
whoops,
let's
see
you
get
something
that
looks
like
that:
a
state,
that's
partly
0
and
partly
1.
This
is
how
we
write
down
a
Quantum's.
B
This
is
direct
Dirac's,
ket
notation,
you
might
have
guessed
from
from
the
from
the
title
of
the
slide
already.
There
is
also
a
thing
called
the
bra
notation,
the
bra
points,
one
way,
the
ket,
the
other
and
you
put
them
together.
You
get
a
bra
ket
how
nice,
when
you
have
two
qubits,
when
you
have
one
qubit,
you
have
two
amplitudes,
because
you
have
two
states
0
and
1.
When
you
have
two
qubits,
you
have
four
states.
You
have
four
amplitudes
0
0
0
1,
1,
0,
1
1.
B
When
you
have
3,
you
have
8
amplitudes
and
you
can
go
on
from
there
exponentially
large
number
of
possibly
implicates
in
this.
There
are
2
to
the
N
elements
in
what
we
call
your
state
vector,
which
describes
the
system
and
each
one
of
those
amplitudes
is
a
complex
number.
When
you
have
n
qubits
in
your
system,
ok,
the
probability
of
measuring.
So
when
you
go
and
you
look
at
this
system,
you
collapse
the
state
so
that
you
find
it
in
exactly
one
of
those
states,
not
the
superposition
of
all
of
them.
B
D
You
know
looking
back
at
Einstein's
paper,
even
if
it
is
incomplete.
That
does
not
get
you
around
this
nonlocality.
These
are
both
theoretical
perspectives
and
then
a
series
of
beautiful
experiments,
one
of
the
earliest
experimenters,
is
honest.
Bay
in
Paris,
really
pointing
out
that
that
these
nonlocality
is,
is
not
these.
What
soon?
As
a
local
hidden
variable
here,
you
cannot
explain
experiments
and
it,
therefore,
we
have
to
sort
of
live
with
this
idea
of
nonlocality.
So
I'll
go
into
a
little
bit
more
detail
now
about
these
kind
of
three
different
comments.
D
So
einstein-podolsky-rosen
this
is
this
1930s
paper.
The
title
of
the
paper
is
quantum
mechanics
completes,
and
so
we
can
understand
that
as
saying
before
we
measure
a
system
does
it
have
a
definite
state,
and
this
is
what
you
heard:
Rob
referring
Rob,
referring
to
when
he's
saying
that
we
are
going
to
do
a
measurement
and
we're
gonna
understand
that
measurement
as
as
a
collapse
into
a
particular
state,
and
so
should
we
think
of
that
system
as
having
had
that
particular
state
before
we
measured
it,
and
so
what
do
we
mean
by
this
kind
of
reality?
D
What
we
would
describe
so
here's
here's
a
quote
from
this
paper.
If
without
in
any
way
disturbing
a
system,
we
can
make
the
certainty
the
value
of
a
physical
quantity.
Then
there
exists
an
element
of
physical
reality
corresponding
to
this
physical
quantity.
So
as
business,
we
talk
about
local
realism,
and
this
is
by
the
realism
part
that
there
is
a
once
we
measure
something
we're
going
to
get
this
particular
answer.
D
He
derives
a
very
specific
inequality
and
it,
and
he
shows
that
if
you
have
a
local
hidden
variable
theory,
it
has
to
satisfy
that
inequality.
And
then
you
can
take
quantum
mechanics
as
we
know
it,
plug
it
in
and
show
that
quantum
mechanical
States
violate
this
inequality.
So
if
quantum
mechanics
is
true,
we
have
to
accept
that.
Then
this
nonlocality
again,
that
was
this
theoretical
perspective
and
then
quite
soon
afterwards,
the
messages
quantum
mechanics
cannot
be
described,
the
local
hidden,
variable
theory
and
yeah.
So
what
do
you
do?
Experimentally
with
that?
D
You
take
the
inequality
and
you
find
ways
to
test
it
in
the
laboratory
and
those
experiments
have
now
been
going
on
really.
For
you
know,
this
is
kind
of
the
fifth
decade
of
experiments
and
the
first
experiments
were
very
beautiful,
but
one
could
also
point
out
ways
in
no
so-called
loopholes
ways
in
which
you
could
still
find
ways
for,
for
maybe
hidden
variables
to
sneak
in
and
the
the
most
kind
of
recent
and
exciting
progress
here
was
was
three
parallel
experiments
in
2015,
which
yeah
I
mean
I'm
close
all
loophole
close
the
major
loopholes.
D
You
know
people
can
always
kind
of
think
of
interesting
loopholes
and
will
continue
to
do
so,
and
that's
very
nice,
but
I
think
that
the
ones
that
people
have
been
most
concerned
about
for
these
felony
qualities
have
been
closed.
Experimentally,
and
so
it's
really
a
beautiful
experimental
demonstration
that
that
quantum
mechanics
is
very
weird
and
and
so
yeah
there's
also
I.
Should
you
know
I'm
talking
about
a
Bell
inequality?
There
are
many
different
kinds:
yeah,
the
most
famous
is
what's
known
as
a
CH
SH
Bell
inequality
for
Clouser.
D
Ian
Holt,
who
wrote
a
paper
on
this
in
1970s,
so
this
comes
to
this-
brings
us
to
these
Bell
States,
and
so
in
the
process
of
deriving
this
inequality,
you
can
kind
of
establish
that
there
are
some
maximally
entangled
states.
These
are
there
some
states,
essentially
that
maximally
violate
these
inequalities
and
so
they're
sort
of
that
the
weirdest
States,
the
most
quantum
states
and-
and
we
give
them
these
names
that
we
always
use
for
them,
this
size
and
and
v,
+
and
and
it's
states
of
two
quantum
bits.
D
So
with
this
notation
that
rod
is
already
introduced,
the
first
0
or
1
is
labeling
the
first
quantum
bit.
The
second
one
is
labeling,
the
second
quantum
bit,
and
so,
for
example,
if
we
look
at
the
first
one,
the
first
state
in
the
upper
left-hand
corner
here,
this
5
plus
state
we're
saying
that
either
both
of
your
quantum
bits
are
in
the
state,
0
or
they're
in
the
state
1.
We
normalize
it
with
the
square
root
of
2.
D
But
the
point
is
that
if
person
a
is
in
possession
of
one
quantum
bit
be
in
possession
of
the
other,
wherever
they
are,
the
that
or
you
know
instantaneously,
we
believe
when
a
measures
her
quantum
bit,
that
we
can
immediately
predict
what
the
outcome
of
these
measurement
will
be.
And
in
this
case,
if
it's
0,
it
will
be
0.
The
end
for
the
four
sigh
plus
and
minus
0
will
be
1.
D
D
And
yet
we
like
to
describe
these
states
as
a
resource
both
for
quantum
communication
and
for
quantum
computation.
So
we
talk
as
I,
suggested
before
about
two
people
sharing
a
bell
pair,
and
when
we
mean
we
mean
that
of
these
two
qubits
one
person
in
possession
of
one
the
other
is
in
possession
of
the
other,
and
that
Bell
pair
is
exactly
what
can
be
used
to
generate
secret
keys
and
that's
kind
of
back
to
what
what
rod
pointed
out
in
his
earlier
slides.
D
You
can
imagine
kind
of
sharing
your
Bell
pair
and
then
either
adding
on
top
of
it,
some
something
like
a
es
which
would
kind
of
or
sharing
many
Bell
pairs
either
adding
on
top
of
it.
Yes
or
the
best
thing
would
be
to
be
able
to
use
those
Bell
tears
in
order
to
generate
a
one-time
pad.
But
of
course
you
would
need
a
very
high
rate
of
Bell
pairs
that
you're
sharing
between
each
other.
D
If
you
have
just
one
Bell
pair,
ideally,
then
that
lets
you
send
one
quantum
state
from
one
person
to
the
other
in
what
what's
known
for
better
or
worse
as
this
quantum
teleportation
and
yes,
so
we
want
to
have
you
know,
suggests
there
I've
explained
that
that
once
one
person
performs
a
measurement
on
her
half
of
this
Bell
pair,
then
that
person
can
predict
immediately
what
the
result
of
the
second
person's
measure
it
will
be.
Does
that
mean
we
can
send
signals
faster
than
late?
D
D
So
we're
trying
to
tamp
that
down
early
on
great,
maybe
there's
some
physics
that
we
don't
know
about,
but
in
the
in
the
physics
that
we're
working
with
now
and
what
the
physics
that
we
understand
to
describe
the
world
that
we
live
in,
it
might
look
like
they're
signaling,
each
other,
but
they're
not
and
the
key.
The
important
thing
is
that,
even
though
person
a
knows
she
can
predict
what
her
partner's
measurement
will
be.
D
That's
not
yet
the
same
as
signalling,
and
they
will
also
need
to
exchange
information
over
a
classical
channel
and
that's
going
to
be
the
bottleneck
in
terms
of
actual
communication
between
the
two
of
them.
So
they're
not
going
to
be
able
to
use
their
quantum
states
in
some
special
way
that
violates
the
that
that
happens
faster
than
the
speed
of
light.
D
I
I
D
So
I
think
this
may
be
I
would
I
would
say
that
we
can't
sort
of
take
shortcuts
with
this
with
this
speed
of
light
story,
so
there's
no
there's
no
tricks
that
we
can
play
there.
I
think
we're
always
limited
to
the
classical
communication,
speed
separately
with
communication.
There
are
really
interesting
ways
that
people
are
exploring
now
in
the
lab
to
use
kind
of
hybrid,
classical
and
quantum
computing
methods,
but
that's
different
than
then
kind
of
harnessing
this
speed
of
light
story.
I
would.
D
B
B
The
idea
is
to
move
a
quantum
state
from
one
place
to
another
to
another.
So
when
we're
talking
about
teleporting,
something
we're
not
talking
about
you're
physically
taking
this
this
camera
or
this
table,
or
something
and
having
it
reappear
in
a
different
place,
we're
just
moving
the
information
that
represents
it
from
one
place
to
another
in
the
quantum
context.
B
So
that's
Charlie-
and
this
is
the
particular
paper
dates
to
a
1993
and
it
was
actually
demonstrated
experimentally,
not
too
long
after
that,
fairly
quickly
by
a
couple
of
groups.
Let's
see
so
what
is
it?
We
got?
Alice
and
Bob.
Alice
has
a
qubit
a
data
qubit,
so
we'll
label
it
D,
and
the
idea
is
that
Alice
wants
to
take
that
quantum
information
and
send
it
from
where
she
is
over
to
where
Bob
yes
sounds
nice
right.
So
how
are
we
gonna
go
about
doing
that?
B
What
we're
going
to
need
is
we're
going
to
need
these
Bell
States
again
we're
not
going
to
go
through
the
math
in
this
particular
part,
but,
as
we
noted
earlier,
you
can
treat
these
as
a
as
a
basis
set
that
will
fill
any
two-dimensional
space
with
complex
numbers,
and
we
take
advantage
of
that
fact
in
the
teleportation
operation.
So
we
start
with
a
single
qubit,
which
is
in
some
state
that
we
don't
know,
maybe
something
we
prepared,
or
maybe
it's
something
that
somebody
else
prepared
and
gave
to
us.
B
We
don't
know
what
it
is,
as
we
already
noted
so,
for
example,
with
this
single
qubit
you've
got
alpha,
is
your
quantum
amplitude
for
the
state
0
and
beta,
is
your
quantum
amplitude
for
the
state
1
the
probability
that
you'll
measure
alpha
or
measure
0
is
the
absolute
value
of
alpha
squared
and
the
probability
that
you'll
measure
1
is
the
absolute
value
of
beta
squared
and
on
the
right
and
at
the
bottom
you
can
see
what
happens
when
you
perform.
Some
simple
operations
is
on
this
that
we
call
the
x
and
z
operations.
B
B
She
takes
this
and
well
sorry,
not
in
this
case,
in
this
diagram,
we're
showing
them
being
created
here
in
the
middle.
So
somebody
else,
a
third
party
is
creating
this,
this
quantum
Bell
pair
to
two
qubits.
We
call
a
and
B
we
take
those
we
distribute
them,
one
to
Alice
and
one
to
Bob.
So
Alice
now
has
two
qubits
the
data
qubit
that
she
wants
to
send
to
Bob
and
this
a
qubit
which
is
a
generic
resource.
B
So
this
is
something
that
you
know
that
the
network
can
make
and
it
is
used
for
it
for
doing
this
teleportation
she
takes
her
qubits
and
she
performs
what's
called
a
Bell
State
measurement,
which
is
a
joint
operation
on
the
two
qubits.
It's
not
the
same
thing
as
measuring
the
two
of
them
independently,
but
when
she
does
this
she's
gonna
get
two
bits
of
classical
data
out
of
it
in
this
case
is
0
&
1
and
she
has
to
send
those
to
Bob.
B
So
it's
moving
the
information
from
this
and
note
that,
even
though,
in
this
diagram
we
drew
a
and
B
coming
from
one
place
and
spreading
out,
there's
not
even
a
requirement
at
the
mathematical
level
that
the
be
the
same
kind
of
physical
qubits
Saudi
could
on
the
Left
could
be
the
state
of
one
of
the
ions
in
Tracey's
laboratory
and
D
on.
The
right
could
be
the
state
of
one
of
the
supercomputer
conducting
qubits
in
Yorktown.
D
B
B
Who
has
come
up
with
questions
over
the
last
of
five
minutes
while
chatting
with
their
neighbor
or
or
otherwise
circulating
blood?
A
little
bit
more
closely?
Somebody's
sucking
and
up
got
a
question.
Come
ask
her,
come
ask
your
questions
and
then
we'll
go
from
there
into
our
implementations.
Oh
we're
not
actually
several
people,
oh.
C
Yeah,
tincho
and
so
I
think
you
said
in
the
last
bit
there
that
you
take
the
bell
pair.
One
part
goes
to
each
party,
yes,
there's
some
computation
or
mutual
observation
that
happens
on
the
left
side
and
then
some
classic
state
bits.
So
it's
some
classic
bits
assent,
I,
eat
normal
data
bits.
Is
that
to
the
far
side,
so
they
are.
There
are
two
million
to
two
data.
B
Bits
two
classical
data
bits
that
get
sent
left
to
right.
Yes,
as
it
happens
because
of
the
way
that
the
operations
that
Alice
performs
those
two
bits
are
guaranteed
to
be
completely
random.
So
there's
no
way
you
can
predict
what
they're
going
to
be
Alice
just
measures
them
and
gets
to
random
bits
sends
those
to
Bob
and
he
uses
them
to
finish
the
reconstruction
of
that
D
State.
J
Actually,
the
way
I
see
it.
This
looks
a
lot
like
information
theory.
What
you
do
is
you
take
an
amount
of
information.
You
do
a
known
operation
on
it.
You
send
that
operation
result
over
the
network
and,
at
the
other
end,
because
you
know
in
common
with
code,
was
used,
you
transform
it
back.
Is
that
a
good
analogy
would.
D
B
B
K
State
your
name,
Robin,
Wilson,
I,
think
I
can
guarantee
I
won't
be
sitting
down.
Saying
yeah
I
understand
this
land,
but
my
question
is
that
in
the
presentation
so
far
it
seems
to
me
that
you
have
treated
quantum
computing
and
quantum
entanglement
is
essentially
the
same
thing,
because
you've
only
talked
about
quantum
computing
and
distributed
nodes.
Will
you
be
talking
about
quantum
computing
on
single
nodes
at
any
point,
or
is
that
something
I
should
just
go
away
and
read
about
not
quite
sure,
I
follow
the
question.
D
One
hand:
by
focusing
for
the
tutorial
on
quantum
networks
in
quantum
of
Peters
we're
sort
of
putting
quantum
computers
to
decide.
You
know
we
might
want
to
use
them,
but
they're,
not
the
focus,
because
there's
something
that
would
happen
at
a
single
node
and
they
wouldn't
be
distributed
in
general
I
would
I
think
we
can
make
the
same
that
you,
the
entanglement
as
a
resource,
would
be
something
we
would
expect
that
you
need
for
a
quantum
computer,
yeah,
yeah,
ok,.
B
D
Didn't
mention
earlier
I'm
I'm
working
me,
the
Institute
for
experimental
physics
at
the
University
of
Innsbruck,
and
we
I'm
the
hardware
person
here,
although
I
don't
usually
think
of
it
as
hardware
I,
think
of
it
as
atomic
physics
or
but
but
yeah
in
this
in
this
audience,
I
think
that's
Wisconsin's
hardware.
So,
let's
think
about
how
I
can
make
my
own
Bell
pair
and
what
we
want
to
remind
you.
We
want
to
come
back
to
this
idea
of
a
quantum
system
with
two
levels
and
an
encode
information
in
those
two
levels.
D
So
we
we
kind
of
look
out
in
the
world
and
we
tried
to
find
systems
where
we
would
have
these
kind
of
two
levels:
0
and
1,
where
we
can
have
these
amplitudes.
That
rods
sketched
out
mathematically
and
you
know,
and
then
we
start
to
get
picky
and
we
say:
well,
we
don't
just
need
a
system
with
two
levels.
What
else
do
I
want?
D
Well,
my
quantum
bits
should
be
something
I
can
entangle
with
one
another
in
some
straightforward
way,
and
we've
also
heard
that
you
want
to
be
able
to
measure
those
quantum
bits
and
actually
in
different
bases.
So
you
want
to
be
able
to
perform
these
different
measurement
sizes.
You
want
to
be
able
to
change
the
phase
in
which
you
measure
the
quantum
bits
in
in.
D
In
this
description,
where
we
said
we
can
describe
two
quantum
bits
in
a
basis
of
these
felt
that
these
four
Bell
States
we
want
to
be
able
to
measure
them
in
all
the
different
bow
States
to
project
them
in
this
linear
algebra
picture
onto
one
of
the
four
Bell
States
and
both
entanglement
and
measurement.
We
want
those
to
be
fast
and
we
want
those
to
be
accurate
and
we
don't
want
to
be
losing
information
to
our
environment.
D
So
we've
drawn
this
very
beautiful,
formal
picture
where
we
only
talked
about
the
quantum
states
and
that's
assuming
that
we
can
isolate
those
quantum
states
from
their
environment,
but
each
kind
of
keep
in
mind
that,
in
that
sense,
entanglement
and
measurement
are
sort
of
at
odds
with
each
other,
because
in
this
beautiful
space
of
entangled
things,
we
want
to
keep
everything
as
far
away
from
the
rest
of
the
world
and
only
have
those
states.
But
as
soon
as
we
talk
about
measurement,
this
is
an
interaction
with
the
rest
of
the
world.
D
So
we
need
to
protect
them,
except
when
we
don't
want
to
protect
them,
and
then
we
need
to
be
able
to
measure
very
fast
right.
This
interaction
with
the
environment
can
can
cause
what
we
would
describe
as
decoherence.
It
would
create
what
what
we've
heard
from
from
Radha
is
a
mixed
state
it
it
reduces
what
we
would
describe
as
the
the
coherence
between
these
different
parts
of
the
quantum
state,
which
again
you
can
think
of
in
sort
of
as
a
phase
relationship
between
waves.
So
it's
nothing
mystical.
D
It's
just
this
wave
picture
here
and
you
want
to
establish
a
definite
phase
relationship
and
when
you
start
adding
other
and
other
systems
into
the
picture,
you
lose
that
phase
relationship.
You
might
also
like
to
be
able
to
move
those
quantum
bits
around,
especially
since
we're
talking
about
networks-
and
you
know
this
might
be
obvious,
but
actually
you
know-
maybe
not
in
this
community,
where
you.
D
You
also
know
that,
as
you
make
your
hardware
smaller
and
smaller
you,
you
run
into
very
physical
defect,
and
so
it's
it's
a
very
sensible
demand
that
one
qubit
should
be
like
another
qubit
that
we
want
to
not
have
to
deal
with
the
idiosyncrasies
of
individual
qubits,
so
yeah,
there's
okay.
This
I
actually
use
an
abbreviation
that
I
got
rid
of
earlier
here
and
I.
Don't
actually
mean
two
level
system
here
so
and
I
failed,
so
two
level
system
referring
to
these
quantum
mechanical
two-level
systems
and
so
yeah.
D
D
Also
yeah,
they
they're
always
moving
right,
and
so
there
might
be
times
we're
drawing
these
sketches
of
quantum
states
for
you
and
you
want
to
say,
put
a
put
a
quantum
state
in
a
box
and
have
it
stay
there
and
for
photons.
The
only
thing
you
could
do
is
have
it
run
around
in
an
optical
fiber
and
eventually
the
losses
in
that
fiber
are
going
to
start
to
catch
up
with
you
atoms.
D
Okay,
so
if
you
want
things
to
stay
in
one
place,
atoms
are
nice
for
that,
and
we
also
have
a
lot
of
tools
with
which
we
can
manipulate
atoms.
We
can
have
very
precisely
controlled
interactions
between
the
electronic
states
of
our
atoms,
using
lasers
or
using
microwaves
depending
on
the
particular
atomic
transition.
So
here
the
two
levels
will
be
about
choosing
different
electronic
States.
We
can
use
these
atoms
for
storage
and
processing,
so
we
can,
that
is.
We
can
not
only
map
States
onto
the
atoms,
but
can
very,
very
precisely
store,
manipulate
information
within
them.
D
I
would
say,
give
it
some
more.
These
are
more
sophisticated
experiments
than
with
photons
in
terms
of
the
hardware.
That's
required
in
terms
of
the
cost
so-
and
this
is
a
plus
or
minus
if
you
don't
want
them
to
go
anywhere.
If
you
want
to
sort
of
build
a
quantum
computer
on
a
tabletop.
D
D
But
this
brings
us
back
to
questions
of.
Are
these
systems
really
identical
with
one
another?
Now
that
we're
fabricating
things
you
know,
if
I
have
a
cesium
atom
I
can
believe
that
it's
gonna
be
identical
to
this
other
cesium
atom
that
I
can
find.
But
you
know
this
gets
a
little
bit
more
challenging
here
with
these
artificial
atoms.
Also,
the
multi-level
structure
that
one
can
fabricate
becomes
a
little
bit
more
complicated
again.
D
Photons
really
seem
like
like
a
very
clear
choice
here,
and
so
this
also
maybe
comes
back
to
the
first
question
that
was
asked
in
the
first
half
of
the
tutorial
about
about
the
role
of
distance,
because
we
can
think
about.
If
we
want
to
make
Bell
pairs,
you
know
what
does
it
mean
to
make
a
bell
pair
and
if
we're
making
them
in
for
making
a
bell
pair
at
a
single
location
in
space
and
then
distributing
that
bell
pair
over
space,
then
we
have
to
think
about
how
we
can
distribute
it
with
the
minimum
loss.
D
Okay,
I
want
to
give
you
a
kind
of
one
slide
on
each
of
these
pictures
on
on
photons
and
atoms.
So,
just
to
briefly
give
you
the
sense
of
how
we
could
encode
0
&
1
in
in
a
photon.
Well,
we
can
use
polarization,
so
we
could
take
advantage
a
boat
of
photons
having
this
property
of
having
two
orthogonal
polarizations.
We
can
use
time
binnen
coatings
did
a
photon
come
early.
Did
it
come
late
and
sort
of
identify
to
discrete-time
bins?
I
D
No
photon
or
I
have
one
and
the
final
one
that
people
often
use
is
a
path
having
two
different
paths
and
saying
that
the
photon
goal
after
did
it
go
right.
This
is
a
picture
from
Jeremy
of
Brian's
science
review
article
back
in
2007,
just
kind
of
some
sketches
where
he
depicts
certain
certain
aspects
of
this
encoding.
D
So
it's
a
here
you
see
in
the
upper
left
hand
corner
a
sketch
of
of
the
two
orthogonal
polarizations
that
you
could
use
for
a
polarization
based
encoding
and
then
the
question
of
how
you
would
do
gate
operations
that
Arad
described
on
your
quantum
bits
here.
So
in
this
case
one
could
use
wave
plates.
This
is
what's
depicted
below.
If
you
can,
you
can
use
half
wave
plates
and
quarter
wave
plates
to
rotate
these
photons
and
those
are
single
qubit
gates.
D
Those
are
changing
the
state
of
a
single
qubit
and
then
in
that
the
fourth
picture,
it's
a
it's.
Actually.
A
picture
of
this
kind
of
path
story
are
actually
converting
between
a
polarization
encoding
and
a
path
encoding.
So
there
are
lots
of
interesting
techniques
for
manipulating
these
photons
as
quantum
bits
and
then
just
a
kind
of
a
glimpse
at
this
idea
about
atoms.
D
So
you
want
it,
you
know
you
have
a
whole
periodic
table
to
choose
from,
and
you
want
to
think
about
two
electronic
states
that
be
well
suited
for
for
for
a
qubit.
So
you
want
to
think
about.
You
know
what
the
lifetimes
are
of
these
states.
D
You,
you
certainly
would
want
to
have
the
both
of
the
states
be
be
relatively
stable,
they
don't
they
don't
need
to
be
infinitely
stable,
and
can
you
manipulate
these
states
easily,
for
example,
with
lasers
that
are
available
off
the
shelf
or
with
microwaves
that
you
can
kind
of
dial
into
and
in
in
the
lab?
Maybe
these
states
are
particularly
robust
with
respect
to
environmental
fluctuations.
Now
would
be
certainly
a
plus.
So
this
is
just
a
picture
here
of
this
is
on
the
right
hands.
D
What's
known
as
a
linear,
Paul
trap
that
we
we
use
in
my
group
and
in
many
other
groups
around
the
world
to
trap
ions,
so
under
ultra-high
vacuum,
we
apply
radiofrequency
to
these
electrodes
of
this
trap
and
we
this
provides
a
potential
well
in
which
we
can
trap
strings
of
charged
particles.
And
if
we
can
use
lasers
to
cool
these
particles,
then
they
actually
stay
in
these
traps
for
days
or
you
know,
even
if
they're
several
days
or
weeks,
depending
on
the
the
conditions
and
the
species.
D
D
Okay.
So
let's
get
back
to
this
plan
of
making
bail
pairs
and
how
would
we
generate
remote
entanglement,
and
so
this
is
I'm
going
to
kind
of
sketch
out
a
couple
of
ways
you
can
do
this.
This
is
an
idea
of
how
to
do
this.
Probabilistically
and-
and
one
idea
would
be
that
you
have
two
atoms
here,
which
again
could
be
these
artificial
atoms
and
you
could
have
each
atom
emit
a
photon.
So
that's
what
you
see
in
this
upper
left-hand
corner
picture
the
atom
at
node,
one
in
the
atom
at
node.
D
2
are
both
emitting
photons
and
so
there's
a
couple
of
variations
here.
One
variation
is
either
the
atom
emits
a
photon
or
it
doesn't.
That
would
be
what
we
call
a
number
state
encoding
of
the
photon,
and
we
could
say
that
maybe
we
could
engineer
it
so
that
the
atom
state
depends
on
whether
or
not
an
emitted,
a
photon.
If
we
use
a
polarization
encoding,
which
is
actually
what
you
see
below
it
should
say
see
instead
of
B
there.
D
If
you
use
a
polarization
encoding
instead
of
the
photons
the
state,
depending
on
whether
or
not
emits
a
photon
and
said
it
will
depend
on
what
the
polarization
was.
But
the
key
aspect
in
both
cases
is
that
the
photon
is
detected
here.
It's
a
single
photon,
that's
detected
in
the
sketch
below
it's
it's
two
photons
that
are
detected,
but
the
most
important
thing
is
that
the
detectors
can't
tell
which
atom
generated,
which
photon
or
if
it
was
a
one
photon.
D
And
that
lack
of
distinguishable
indistinguishability
means
that
the
detection
event
actually
projects
the
atoms
into
an
entanglement
entangled
state.
So
we
would
say
that
this
act
of
measurement
prepares
an
entangled
state
between
these
two
atoms.
So
that
sounds
actually
kind
of
easy.
You
can,
you
know,
kind
of
get
each
of
two
atoms
to
make
a
photon
and
you
need
to
measure
the
photons
and
then
they
sort
of
turn
up
entangled
and
yeah.
D
This
is
again,
as
I
said,
the
key
principle,
this
indistinguishability
from
the
perspective
of
the
detectors,
and
so
the
the
first
experiments
on
this.
This
really
pioneering
experiments
were
done
at
the
University
of
Maryland
or
actually
originally
at
University
of
Michigan
and
Kris
Munroe
I
was
the
principal
investigator
is
now
at
the
University
of
Maryland
or
the
joint
quantum
Institute,
and
he
in
a
series
of
experiments
for
kind
of
more
than
a
decade.
He's
done
exactly
this.
D
D
Radiofrequency
voltages
to
this
trap
in
order
to
confine
ions
in
this
very
small
space
in
between,
and
actually
they
have
two
different
traps
here
in
this.
This
is
a
picture
taken
from
their
2015
paper,
where
they
have
traps
separated
by
a
couple
of
meters
and
in
each
of
these
boxes,
they're
achieving
ultra-high
vacuum
conditions.
You
know
that,
are
you
know
twelve
orders
of
magnitude,
thirteen
orders
of
magnitude
lower
than
atmosphere
in
one
of
their
vacuum
chambers.
D
D
The
left
one
here
and
the
right
one
there
and
those
they
can
identify
with
their
quantum
bit
and
then
they
have
a
scheme
where
they
use
a
laser
to
excite
the
atom
and
it
either
decays
in
one
direction,
to
one
state
or
in
the
other
direction
to
the
other
state
generating
different
polarizations.
And
basically
they
can
do
some
measurements
I'm
not
going
to
and
happy
kind
of
later
on,
to
go
into
the
details
of
what
it
means,
but
they
can.
They
can
characterize
their
system
in
such
a
way
that
that
proves
that
they
can
have.
D
They
have
entanglement
first,
they
can
show
entanglement
between
the
atoms
and
the
photons,
and
then
this
is
actually
the
basis
for
their
entangling.
The
two
remote
atoms
here,
so
these
are
measurements
that
show
the
atoms
are
entangled
with
one
another,
and
rod
already
mentioned
this
idea
of
a
state,
fidelity
or
a
fidelity
and
from
again
from
a
linear,
algebra
point
of
view.
D
This
was
a
experiment
where
they
were
generating
entanglement
five
times
a
second
four
times
a
second,
and
that
was
an
improvement
of
I,
think
eight
orders
of
magnitude,
so
they
had
from
their
2007
paper.
You
know
so
on
one
hand
we
have
just.
You
know
incredible
improvement
over
the
course
of
a
decade,
but
in
terms
of
rates
that
you
can
then
use
to
generate
one-time
pads,
we're
still
a
long
way
off
yeah.
D
So
that's
a
story
about
ions
which
of
the
things
that
I
know
best
experimentally
in
this
context,
but
over
the
past
decade
decade
and
a
half,
there
have
been
examples
of
remote
entanglement,
very
similar
experiments.
Sort
of
demonstrated
in
in
you
know
a
handful
of
different
settings,
and
also
in
a
few
of
these,
has
not
only
remote
entanglement,
but
also
teleportation
has
been
demonstrated.
D
So
in
this
picture,
I
showed
you
here
we
had
the
two
quantum
bits
above
and
the
one
below
which
looks
very
similar
to
the
picture
that
you
saw
from
rod
where
you
can
then
use
the
entanglement
between
the
pair
of
the
one
above
and
the
one
below
in
order
to
teleport
a
state
between
the
two
chambers.
That's
been
done
with
the
ions,
with
neutral
atoms,
spin,
demo,
superconducting,
qubits
and
Envy's
actually
I
think
not
the
asylum,
solemn
walls,
but
pretty
much
at
least
three
of
the
systems
here.
Yeah.
D
What
I
also
want
to
emphasize
here
is
that
the
state
of
the
art
yet
now
consists
of
two
node
experiments
and
and
really
kind
of
you
know-
maybe
two
systems
over
here
on
one
side
and
once
a
story
here,
where
I'm,
limiting
myself
to
a
discussion
of
things
that
are
really
physically
separated.
So
yeah
there's
been
a
lot
of
progress
but
and
and
we're
looking
forward.
You
know
we
know
that
we
as
a
community
really
need
the
kind
of
help
of
people
thinking
about
networks,
but
we
don't
yet
have
those
networks
in
place.
D
H
D
Why
doesn't
it
write
this
straight
yeah,
so
yeah
I
mean
so
something
gets
it's
interesting
right.
Something
gets
destroyed.
So
at
the
start
you
had
you
had
an
atom
and
a
photon
say
over
here
and
you
had
an
atom
and
a
photon
over
here
and
you
measured
the
two
photons
and
the
measurement
was
destructive,
so
the
photon
state
is
the
photons
are
gone.
They
were
absorbed
by
your
detector
and
and
and
they're
they're
lost,
and
also
the
entanglement
that
you
had
between
the
atoms
and
the
photons.
D
If
you
know
that
that's
lost,
there
are
also
schemes
that
don't
rely
on
entanglement,
but
if
it
was
a
scheme
based
on
the
entangle,
what
you've
lost
that
entanglement
and
so
yeah
you
did
get
rid
of
something
in
your
measurement,
but
you
also
were
able
to
harness
this
indistinguishability
in
order
to
create
entanglement.
L
This
is
Dave
wheeler,
one
more
question,
so
you
talked
about
the
rate
at
which
entanglement
was
was
happening
and
I
think
you
said
you
know
five
times
a
second
or
something
like
that
and
that's
an
improvement.
What
is
the
sort
of
speed
or
velocity
that
we're
at
in
in
actually
improving
that
and
getting
to
the
point
where
we
can
get?
You
know
thousands
of
qubits
or
tens
of
thousands
of
qubits
and
tangled,
and
is
that
something
that
is
on
the
horizon
or
is
that
something
that
we
still
see
as
several
decades
away.
D
We
also
think
we
should
be
able
to
talk
about
kind
of
kilohertz
rates,
but
yeah,
and
then
you
can
get
more
speculative
about
how
you
keep
scaling
that,
but
but
it
seems
like
first,
you
want
to
kind
of
get
that
improvement
additionally,
having
long,
you
know
thousands
of
qubits
separately.
That
also
seems
very
promising,
but
then
combining
different
improvements
can
also
be
a
challenge
or,
for
example,
there
are
ways
that
you
know
extending
the
this
so-called
coherence
time
that
is
reducing
the
interaction
of
the
environment.
D
B
All
right,
let's
see
so
a
couple
of
quick
things,
I
forgot
to
mention
right
at
the
beginning,
occurred
to
me,
while
the
Tracy
was
talking
number
one.
The
slides
for
this
are
up
in
the
data
tracker
website,
I
uploaded
them
in
both
PDF
and
PowerPoint
format,
and
both
of
the
files
are
kind
of
large.
So
tens
of
megabytes,
unfortunately,
because
of
all
the
pictures
and
whatnot
there's
a
huge
appendix
in
this
we're
only
using
about
half
of
the
slides
of
this
and
there's
a
huge
appendix
with
a
bunch
of
the
math
in
it.
B
So
if
you
want
that,
you
can
get
it
and
take
a
look
through
that
as
we
go
and
second,
while
Tracy
was
talking,
I
looked
up,
yes,
the
the
title
of
mark.
Well,
while
these
book
is
just
quantum
information
theory
keep
in
mind
that
that's
an
information
theory,
primer
or
textbook,
not
not
an
introduction
to
quantum
computing
and
certainly
not
an
introduction
to
quantum
networking.
So
if
you
like
in
for
classical
information
theory
you'll
like
that
book
all
right,
so
we
saw
this
earlier
on.
B
What's
the
job
of
a
quantum
repeater,
it's
to
make
this
base
level
entanglement
over
a
link,
which
is
what
Tracy
just
talked
about
the
ability
to
couple
entangled
links
along
an
end
in
a
and
paths
to
meet.
The
applications
needs
to
build
that
to
monitor
and
manage
the
errors
and
to
participate
in
the
management
of
the
network
as
a
whole.
So
what
do
we
have?
Well
conceptual
hardware:
you've
got
you
know
a
series
of
nodes
and
each
one
has
inside
of
it.
B
Some
set
of
stationery
member
is
stationary
memories,
a
qubit
which
you
know
I've
drawn
using
the
atom
symbol
here,
and
these
stations
are
separated,
perhaps
by
tens
of
kilometers
they're,
not
separated
by
thousands
of
kilometers.
Generally
speaking,
they're
they're
pretty
short
distances
as
we
go.
So
how
do
we
build
entanglement
from
one
to
the
end
of
this
chain
to
the
other
that
what
we're
trying
to
accomplish
go?
There
are
also
all
optical
approaches
to
doing
this,
with
no
stationary
memories
at
all,
we're
not
going
to
talk
about
those
they
have
their
own
set
of
challenges.
B
Unfortunately,
that's
not
gonna
work.
Why
you
take
those
individual
photons
and
you
put
them
in
a
fiber
and
you
lose
them
and
you
do
it
again
and
you
lose
it
and
then
eventually,
maybe
you
succeed
in
getting
one
through
the
through
the
the
fiber
here
and
to
end,
but
the
loss
in
the
channel
is
always
going
to
be
high.
It's
always
going
to
be
too
high
to
actually
encode
information
and
put
this
on
it.
Well,
always
for
a
very
long
time
now,
we'll
talk
just
a
little
bit
about
that
later.
B
So
we
have
to
find
some
way
of
dealing
with
this
with
this
tremendous
amount
of
loss
in
this.
That
means
we're
gonna
wind
up
using
some
sort
of
acknowledge
to
link
layer,
axial
Dahlberg
who's
around
here
to
axel,
stick
your
hand
up
so
Axel's
over
there
he's
from
Stephanie's
group.
He
gave
a
presentation
in
Bangkok
on
some
of
their
hardware
roadmap
stuff,
and
he
also
has
an
internet
draft
on
a
protocol
for
link
architecture
stuff
and
we're
gonna
talk
about
that
tomorrow
during
the
during
the
meeting.
B
But
you
need
to
essentially
build
entangle
to
build
and
acknowledge
to
link
layer
in
order
to
make
this
whole
thing
work.
We
can
draw
this
sort
of
timewise
and
sort
of
a
with
time
going
down
the
vertical
axis.
You
know
top
to
bottom
and
you're,
just
as
going
left
to
right
there.
We
can
draw
this
as
sort
of
a
gray
trapezoid,
something
that
looks
like
that.
B
If
you
put
a
bunch
of
them
together,
you
might
imagine
stringing
them
into
a
series
of
things
like
this,
and
maybe
we
can
acknowledge
them
as
we
go
and
do
sort
of
hop
by
hop
teleportation.
Even
though
we
couldn't
really
just
put
on
an
individual
photon
and
send
it
from
one
place
to
the
other,
as
we
go
hop
by
hop,
maybe
we
can
do
teleportation
hop
by
hop
the
problem.
Is
this
takes
long
memory
lifetimes
and
the
fidelity
of
the
operations?
B
Several
different
repeater
schemes
have
been
defined.
I
listed
five
of
them
here
that
paper
I
just
showed
you
from
Murali
Duran
and
from
on
John's
group
that
they
defined
essentially
three
generations
of
networks,
I
call
them
1g,
2g
and
3G
1g
uses
what
we
call
purification
and
uses
what
we
call
entanglement
swapping
over
acknowledged
links.
This
is
truly
a
distributed
computation.
This
is
not
store-and-forward.
This
is
not
simple
data
plain
stuff,
like
you,
haven't
any
classical
internet
router.
This
is
end-to-end
a
distributed.
Computation
2g
is
all
right.
B
Let's
do
something
more
sophisticated,
let's
apply
error
correction
to
this
over
acknowledged
links
and
then
it
does
become
a
little
bit
more
akin
to
it
to
store-and-forward,
but
really
you
get
into
that
when
you,
when
your
success
probability
for
doing
this,
gets
to
the
point
where
you
can
live
without
the
acknowledgments
on
the
link
layer
and
then
you
can
do
what's
called
a
a
3G
network
for
doing
this.
So
this
first
generation,
this
quantum
repeater
operation,
I've,
got
three
stations
here:
zero
one
and
two
one
has
one
qubit
station
one
in
the
middle.
B
There
has
two
qubits.
So
what
we
do
is
we
use
the
link
to
make
entanglement
between
station
0
and
1,
and
we
use
the
other
link
to
create
an
entanglement
between
station,
1
and
2,
and
then
we
execute
again
one
of
these
things
labelled
mistake
measurement.
This
operation
is
very
much
like
teleportation.
You
could
in
fact
consider
it
to
be
a
form
of
teleportation.
B
This
destroys
the
two
qubits
in
the
middle,
but
it
doesn't
destroy
the
two
qubits
on
the
end
and
if
this
works
properly,
what
you're
left
with
is
entanglement
between
the
two
endpoints.
This
process
is
what
we
call
entanglement
swapping
now.
Unfortunately,
this
does
introduce
errors,
it
reduces
the
fidelity
of
our
system
and
so
you're
going
to
have
to
apply
some
error
or
management
techniques
on
top
of
those.
But
this
is
the
key
technique
to
get
beyond
a
single
hop.
B
That
has
to
be
done
for
that,
but
this
introduces
errors.
So
how
are
we
going
to
deal
with
this?
The
standard
technique
which
people
have
actually
begun
to
demonstrate
experimentally
is,
what's
called
purification,
I
think
Tracy's
going
to
talk
about
that
here
in
just
a
couple
minutes.
This
purification
is
a
form
of
error
detection.
This
is
not
error.
Correction.
B
It
increases
your
confidence
about
that
that
remaining
bellperre
and
you
have
said
with
higher
probability.
We
believe
the
the
entangled
stage
is
actually
good.
So
dealing
with
all
this.
You
could
call
this
you.
We
can
define
this
in
terms
of
a
a
protocol.
Stack
you're
gonna
have
physical
entanglement
at
the
bottom
and
what,
at
the
time,
I
called
EC
the
entanglement
protocol,
the
entanglement
control
protocol
back
in
the
paper
we
had
in
transactions
on
networking
10
years
ago
now,
Wow
10
years
ago.
B
Oh,
and
then
you
have
some
some
software
that
will
do
purification
control
and
you
got
some
some
protocol
that
will
do
entanglement,
swapping
control
and
then
maybe
purification
control
again
and
then
ultimately,
application.
On
top
of
this
note
that
these
two
here
at
the
bottom,
they
will
operate
over
distance,
one,
the
others
repeat
at
different
distances,
so
you're
doing
entanglement
swapping
over
or
two
hops
and
then
four
hops
and
then
a
Thompson
16.
B
You
also
have
to
repeat
the
purification,
because
at
each
level,
where
you're
doing
this
you're
introducing
new
errors
and
then
ultimately,
finally,
hopefully
one
purification
end
to
end
and
then
the
application
level.
All
the
way
at
the
end,
note
that
the
only
quantum
part
of
all
of
this
is
right
there
at
the
bottom.
Everything
else
above
that
is
classical
networking
stuff
and
that's
why
everybody
in
this
room
is
needed
to
actually
commit
to
actually
build
this,
because
when
you
put
this
together,
you
know,
as
I
said,
these
things
are
a
true
distributed.
Computation
right.
B
You
take
this
even
over
four
hops
you're
going
to
have
a
complicated
set
of
interactions
between
the
four
hops
for
managing
these
some
of
the
operations
over
one
hops,
some
of
them
over
two
hops,
some
of
them
over
four
ups,
as
you
go,
some
of
them
you're
the
end
to
end
as
you
go,
alright,
so
2g
and
3G
s,
that
was
one
gene
networks,
2g
and
3G
are
still
very
far
away.
Even
1g
is
very
hard.
You've,
probably
gotten
an
idea
from
what
Traci
talked
about
the
entitlement.
Success
probability
is
low.
B
There
are
many
round
trips
involved.
The
protocol
does
you've
only
got
a
few
cubits
per
node.
The
memory
lifetimes
are
still
problematic
and
when
you
want
to
do
entanglement
swapping
getting
a
successful
entanglement
between
Alice
and
Bob,
at
the
same
time
that
you
have
one
between
Bob
and
Charlie
in
order
to
make
that
entanglement
swapping.
That's
one
of
the
current
challenges,
experimentally,
for
what
people
are
actually
doing.
B
2G
is
going
to
blow
up
the
resource
requirements
by
an
order
of
magnitude
give
or
take,
and
the
biggest
problem
that
we
have
besides,
that
is
in
the
existing
quantum
computers
and
in
the
laboratories.
The
operations
themselves
are
not
yet
good
enough
to
make
for
long
error,
correction,
work
or
actually
getting
close
to
that,
but
we're
not
there
yet
for
3G.
B
Not
only
are
you're
gonna
have
to
have
error
correction
that
works
and
a
lot
of
memory
at
each
one
of
these
nodes,
but
you're
also
going
to
have
to
have
the
probability
of
80
to
93
percent.
Depending
on
your
choice
of
code
in
getting
every
single
photon,
you
Pat
you
put
into
the
fiber
out
the
other
end
and
detected
properly,
and
you
let
it
wonder
the
current.
What
are
the
current
success
rates
in
your
laboratory
for
actually
detecting
a
photon
that
comes
out
of
an
atom.
D
D
These
days,
you
can
buy
really
nice
expensive
detectors
that
get
you
very
close
to
a
hundred
percent,
but
for
a
long
time
the
detectors
themselves,
50
percent
and
for
telecom,
it's
worse,
so
yeah.
So
so
then
right
you're
already
kind
of
killed
with
just
the
detection
stuff.
So
that's
a
very
new
thing
that
the
detection
stuff
doesn't
tell
you
right
away.
So
you.
B
Gotta
get
from
there
from
this
five
to
10%
she
can
achieve
in
the
lab
today
to
80
to
90%
success
rate
and
detecting
every
single
photon,
so
those
three
gene
networks,
which
would
be
real
store
and
forward
networks.
The
same
way
the
data
plane
on
the
internet
runs
today.
Those
are
a
long
ways
away
all
right.
Let's
see
you
want
to
do
this
business.
D
This
is
really
fast
because
it's
the
perspective
on
experimentally,
where
we
are
on
these
repeaters
and
yeah
we're
not
very
far,
and
so
I'm,
just
gonna
kind
of
capture
that
for
you
and
we're
gonna
kind
of
have
a
little
recap
of
what
these
repeaters
were
looking
like.
So
so,
hopefully
it's
a
quick
reminder,
so
we
think
about
lets.
You
know
when
we
hear
from
theorists
as
experimentalist
when
we
hear
kind
of
from
fierce
about
this
second
generation
third
generation.
D
You
know
it's
very
interesting,
intellectually,
but
you're
also
kind
of
like
really
are
you
kidding,
so
you
know,
1gi
looks
from
our
perspective
hard
enough,
and
and
so
what
would
that
look
like
for
these
ions?
Well,
what
you
would
do
is
entangle
one
pair
of
ions
in
the
same
way
that
I've
already
showed
you.
D
So
you
would
have
a
single
ion
here,
for
example,
that
gets
entangled
the
photon,
a
single
and
that
gets
entangled
another
photon
on
the
right-hand
side
and
then
this
beam
splitter
is
supposed
to
show
you
that
we're
racing,
the
information
about
which
paths
each
photon
came
from
and
then
there's
some
detectors
that
I
left
out
of
the
picture.
So
you
would
entangle
those
two
ions
on
the
left
and
you
would
entangle
the
other
two
ions
on
the
right
and
then
you
would
do
this
bail
measurement.
D
That
rah
talked
about
on
the
two
central
ions
and
that
bail
measurement
would
then
entangle
the
outermost
two
ions,
so
I
haven't.
Given
you
any
sense
of
how
that
we
do
this
bail
measurement
in
practice
on
the
ions.
Maybe
I
can
try
to
kind
of
give
you
the
the
30-second
version.
The
the
key
is
that
we
think,
because
these
ions
are,
on
the
one
hand,
repelling
each
other
and,
on
the
other
hand,
trapped
in
the
same
trap.
You
think
about
them.
You
know
like
a.
D
We
would
describe
them
as
a
coupled
harmonic,
oscillator,
they're
kind
of
pendulum
and
they're
coupled
to
each
other
and
they're
swinging
together.
So
their
motion
is
linked
to
one
another.
They
have
shared
motion
and
we
can
use
this.
What
we
would
talk
about
his
emotional
bus,
so
we
can
on
one
hand
we
have
access
to
the
electronic
states
of
the
ions
and,
on
the
other
hand,
to
their
motion,
and
we
take
advantage
of
that
in
order
to
manipulate
the
joint
states
of
the
ions.
So
we
can
do
measurements.
D
We
can
project
the
state
of
these
ions
into
one
of
the
four
bail
bases
and
what
we
do
in
the
end
is
we
illuminate
the
ions
with
certain
laser
light.
We
look
at
fluorescence
and
based
on
those
fluorescence
measurements.
In
our
manipulations,
with
lasers,
you
can
say
worth
ayyyye
one
which
one
of
these
four
Bell
states
are
the
ions
in
okay.
So
this
Bell
measurement
on
the
ions
in
the
middle
then
entangles
the
ions
outside.
So
this
is
if
you're
yeah
still
a
week
after
a
couple
of
hours.
D
In
a
long
day,
you
learned
already
that
this
is
what's
called
entanglement.
Swapping
and
it's
really
nice,
and
so
our
tendency
is
to
start
to
chain
together
a
bunch
of
these
things.
But
this
is
approach.
That's
not
scalable,
because
these
errors
are
going
to
accumulate.
All
of
these
steps
will
have
intrinsic
errors
and
when
we
start
to
concatenate
things,
it's
going
to
go
downhill,
so
the
approach
would
be
entanglement
purification.
D
So
you
know
what
we
should
remember
is
that
this
idea
of
a
quantum
repeater,
at
least
in
the
first
generation
you
think
of
it
as
entanglement
swapping
plus
purification
and
the
key
concept
of
purification,
is
that
you
have
multiple
copies
of
entangled
pairs
which
allow
you
to.
Then
you
can
start
sacrificing
some
of
your
copies
in
order
to
get
a
higher
fidelity
and
you
need
to
be
able
to
do
gate
operations
between
between
pairs
of
local
qubits.
D
So
here's
again
this
again
I'm
trying
to
think
of
a
minimal
instance
where
you
could
have
not
only
entanglement
swapping
but
also
purification,
so
that
now
we,
let's
think
about
an
instance
where
we
have
not.
We
double
everything.
So
we
have
two
ions
over
here
for
ions
in
the
middle
two
ions
there,
and
then
we
would
entangle
these
two
pairs
of
ions,
so
pairwise
entanglement
on
the
Left
pairwise
entanglement
on
the
right.
D
We
would
do
a
two
bowel
measurements
here
and
then
we
would
have
two
entangled
pairs
between
the
left
and
the
right
hand
side
and
then
would
come
this
final
step
of
the
purification.
What
we
would
do
is
we
would
do
what's
called
a
parity
measurement
of
the
ions.
We
would
ask,
on
the
left
hand,
side
are
the
ions
both
in
the
same
state.
D
Are
they
in
an
in
in
opposite
states,
and
we
would
also
ask
that,
on
the
right
hand
side,
then
we
would
have
classical
communication
to
share
that
information
and
based
on
the
joint
outcomes.
We
would
either
throw
away
the
the
pair
or
we
would
if
we
got
the
outcome
that
we
liked,
and
we
would
know
that
the
purity
had
sort
of
I
had
increased,
or
at
least
the
chances
that
the
period
that
we
have
a
highly
entangled
state
has
is
increased
at
the
cost
of
sacrificing
one
of
those
pairs.
D
So
we
do
a
measurement
that
sacrifices
one
of
our
two
ions
on
either
side
and
in
the
end
we
end
up
with
a
pair,
that's
more
highly
entangled,
and
so
you
can
show
that
this
would
then
be
a
scalable
thing
with
purification.
If
you
can
brakes
meet
certain
bounds,
you
could
then
start
to
concatenate
these
systems.
D
Yeah
I
think
this
is
the
simplest
story.
So
in
a
nutshell,
repeater
is
entangled
chopping,
close
purification.
We
have
to
wait
for
classified
information
to
travel.
The
simplest
version
would
be
what
I've
sketched
here.
Eight
qubits
three
nodes
and
you
need
these
gate
operations
and
the
so
nobody's
done
it.
That's
what
you
should
take
away.
D
People
are
working
really
hard,
I,
think
it's
quite
likely
than
in
the
next
two
or
three
years,
we'll
have
a
cut
of
a
first
proof
of
principle:
experiment,
the
closest
experiment
so
far,
I
wish
I
could
tell
you
it
was
with
ions,
but
it's
actually
with
nitrogen
vacancy
centers
and
Ronald
Hanson's
group
at
Delft.
So
these
diamonds,
where
you
replace
one
of
the
carbons
with
a
nitrogen
and
they've,
done
purification
of
entanglement
with
for
qubits
yeah.
So
in
beautiful
experiments
there
maybe
I'll
pause
there.
I
D
I
D
Be
done
in
parallel
and
that's
a
very
yeah,
so
here
what
you
end
up
at
the
end
with
is
a
single
Bell
pair
of
to
remote
qubits,
which
you
could
use
to
teleport
a
single
qubit
and
then
here
I
sketch
in
parallel
and
that's
really
platform
dependent.
So
I
would
argue
that
ions
are
a
nice
system
for
doing
this
kind
of
thing
in
parallel
and
it
will
depend
on
the
system
how
well
you
can
parallelize
it.
M
Hi
Juan
Carlos
Sonia
I
was
a
little
worried
when
I
saw
the
diagrams
of
the
protocol
stack
and
the
GS
and
kind
of
remind
me
my
nightmares
about
3gpp
and
sa-2
and
things
that
I
don't
want
to
feel
and
live
here.
But
I
was
even
more
worried
when
I
started
thinking.
You
know.
Disruptive
waste
like
in
this
repeater
is
there
a
way
that
you
can
start
foreseeing
that
there
will
be
attacks
of
a
man-in-the-middle.
B
That's
part
of
that's
dependent
on
the
fact
that
that
we
actually
are
doing
more
of
the
checks
and
to
end,
and
so
those
end-to-end
checks
will
determine
that
the
kinds
of
states
that
are
left
after
these
operations
are
exactly
two
qubit
entangled
States.
If
somebody,
for
example,
you
know
the
man
in
the
middle
tries
to
sneak
in
and
entangle
a
third
qubit
with
it
that
shows
up
in
the
statistics
for
the
tests
that
are
actually
done
in
two
end.
We
can
prove
that
this
isn't
a
two
qubit
entangled
State.
B
We
might
not
know
for
certain
whether
it's
three,
whether
it's
three
cubits
or
whether
it's
just
been
busted-
and
we
don't
know
what
the
problem
is.
But
we
know
it's
not
a
good
two
qubit
state
and
conversely,
we
know
when
we
do
know
that
we
have
them.
We
know
that
the
path
is
working
end
to
end
and
it
doesn't
matter
what's
happening
in
the
middle
and
it's
always
yes.
Okay,
thanks
actually.
M
H
N
Floor
you
know,
for
that
security
guarantee,
yet
to
make
sure
that
class
whole
bits
that
you
are
actually
sending
back
and
forth,
but
you
don't
show
I
actually
been
authenticated,
but
actually
wasn't
my
question.
N
My
question
was
really
about
how
many
purification
steps
you
need
to
do
for
each
round
is
that
it's
obviously
gonna
be
somewhat
fixed,
based
on
how
strong
how
good
your
fiscal
layers
are,
however,
free
they
are,
but
are
typically
how
much
how
many
times
you
have
to
expect
before
you
get
good
enough
to
be
able
to
go
up
to
the
next
level.
N
B
Actually,
a
really
good
question,
the
I
would
say:
go
read
my
transactions
on
networking
paper
from
2009
and
that
will
actually
give
you
I
think
a
good
framework
for
how
to
think
about
that,
but
that
particular
paper
was
built
on
top
of
a
simulation
of
a
of
a
particular
type
of
system
that
nobody's
really
trying
to
build
anymore.
So
so
the
specific
numbers
that
are
in
that
paper,
I
would
say,
are
outdated.
You
have
you
have
something
more
about
the
current
stuff.
D
Oxford,
where
they've
looked
at
very
sort
of
state-of-the-art
fidelities
for
ion
photon,
entanglement
and
shown
that
that
those
are
kind
of
reasonable
for
for
scaling,
so
I
know
that
they
maybe
have
numbers
there.
That
I
don't
have
in
mind
about
how
many
purification
steps,
but
absolutely
so
the
the
better.
Your
states
are
to
start
with
the
fewer
steps
you'll
need,
and
if
you
have,
if
you
have
really
you
know,
states
that
are
quite
close
to
class
flow,
you
would
need
sort
of
a
prohibitive
number
of
steps.
That's.
C
B
B
If
you
want
to
do
real
distributed
computation,
you
need
high
90s
of
fidelity,
and
so
that
means
all
not
only
that
you
have
your.
Your
hardware
has
to
be
really
good
for
the
purification
that
you're
doing,
but
it
also
means
that
you,
wind
up
spending
a
lot
of
resources
to
do
what's
called
tomography
to
test
the
system,
to
see
how
good
it
is,
the
better
the
system
is,
the
more
you
have
to
test
it,
to
figure
out
what
the
error
rate
is.
C
D
Benchmark
my
system
and
then
I
want
to
do
this
and
I
have
to
hope
that
it
didn't
change
from
what
I
benchmarked
it
or
do
I
have
to
how
much
do
I
have
to
interrupt
it
to
benchmark
it
while
I'm
running
it,
and
how
much
does
that
cost
me
in
terms
of
resources
yeah?
So,
okay,
with
that
outlook
on
on
you
know,
what
we
hope
is,
will
be
demonstrations
in
the
next
few
years
of
building
blocks
for
quantum
computers.
D
B
Just
to
give
you
an
idea
of
what
sort
of
things
are
where
the,
where
things
are,
we
have
done
some
work
on
network
architecture
based
on
Joe
touches,
recursive
network
architecture.
For
those
of
you
who
know
Joe
the
protocol
stuff
that
we
already
talked
about
a
little
bit.
We've
done
some
work
on
routing,
we've
done
some
work
on
multiplexing
and
control
in
larger
networks,
and
we've
done
some
work
on
internet
working.
This
was
part
of
shota's
PhD
thesis.
If
we
had
two
different
kinds
of
networks,
how
would
we
connect
them
together?
B
As
as
we
go
from
individual
networks
toward
toward
an
Internet,
and
we've
done
some
work
on
the
security
of
systems?
What
happens
when
somebody
actually
takes
control
of
one
of
these
repeaters?
Do
they
have
more
capabilities
than
they
would
have
in
a
classical
system?
We've
done
some
work
on
resource
analysis
for
applications,
and
we've
done
some
work
on
the
quantum
equivalent
of
network
coding.
B
So
that's
sort
of
you
know
the
range
of
things
that
that
people
have
been
working
on
for
the
last
few
years
from
Stephanie's
group
axel
gave
me
that
gave
me
this
list
of
things.
They've
been
working
on
link
layer,
protocols
and
parameter
regimes
for
dealing
with
this
and
how
you
actually
go
about
using
this
for
particular
applications
and-
and
you
know,
a
bunch
of
different
stuff-
they
built
some
simulators
for
doing
this.
B
I
B
I
B
From
this,
but
there's
been
a
community
of
people
working
towards
satellite
based
experiments
forever
for
what
no
more
than
10
years
now
and
they've
done.
Even
some
experiments
in
orbit
saying
hey.
Maybe
we
could
do
some
stuff
with
this
and
then
bang
two
years
ago
of
the
team
from
China
produced
a
really
fantastic
paper
showing
that
they
can
generate
two
entangled
photons
in
orbit
and
send
them
to
earth
and
detect
those
two
photons
and
prove
that
they
had
entanglement
had
two
ground
stations
1,200
kilometers
apart,
was
it
in
China,
something
like
that?
Yeah.
D
I
D
Really
I
guess
more
than
hundred
kilometers
at
any
free
space,
experiment,
yeah
and
I.
Guess
I
would
picture
those
as
having
separate
applications
that
the
the
free
space
or
satellite
based
experiments
or
satellite
based
encoding
can
get
you
over
these
really
long
distances
right
can
get
you
global
connections,
but
I
guess
we
can
think
about
applications
where
the
connections
will
be
so
local
and
not
certainly
the
resources
of
satellites
you're
not
gonna,
have
so
many
yeah,
especially
for
things
like
maybe
a
more
local
distributed
quantum
computing.
We
would
imagine
that
as
being
fiber
based
yeah.
D
B
They
used
to
to
telescopes
on
to
two
mountains
140
kilometres
apart
or
something,
and
that
in
some
ways
is
actually
harder
than
going
to
a
satellite,
because
140
kilometres
of
air
really
distorts
thing
things
terrifically,
whereas
if
you're
going
vertically,
you
only
got
to
go
through
about
ten,
but
then
you
have
to
hit
a
satellite
that's
moving
in
orbit
and
at
the
conference
the
Tracey
and
I
helped
run.
Two
years
ago
we
had
the
speaker
from
who
is
the
chief
engineer
from
from
the
satellite
group
that
did
that,
and
they
have
to
point
the
telescope.
B
B
Let's
see
all
right
so
just
some
stuff,
some
good
repeater
references
you've
already
seen.
We've
already
talked
about
some
of
these,
though
there's
the
list
for
what
you
want.
If
you
want
to
learn
more
about
the
basics
of
quantum
computing,
I
have
an
online
course.
I
have
a
MOOC
called
called
understanding.
Quantum
computers
and
the
next
run
of
that
actually
starts
April
1st
next
Monday
the
course
is
free.
B
Unless
you
want
the
certificate-
and
you
probably
don't
want
the
certificate,
we
have
subtitles
all
of
its
in
originally
English,
but
but
we
have
subtitles
in
Japanese
and
in
Thai,
and
if
anybody
wants
to
translate
it
in
other
languages,
we
would
be
happy
to
have
that
done
as
well,
and
Stephanie
VanArsdale
fee
has
a
MOOC
on
quantum
internet
stuff
which
I
have
not
gone
through.
Have
you
yeah,
so
I
can't
tell
you
anything
at
all
about
the
quality
of
it,
because
I
haven't
looked
at
it
axel?
B
Have
you
have
you
used
to
the
course
the
any
comments
on
it,
but
he's
thumbs
up
right,
of
course,
she's
his
PhD
advisor
so
right,
it's
gotta
be
gotta,
be
thumbs
up
great
I'm
certain.
It's
excellent
I,
just
haven't
had
a
chance
to
look
at
it
and
if
you
want
more
on
quantum
computing,
so
our
MOOC
is
intended
doesn't
have
a
lot
of
math
in
it.
It's
intended
to
take
you
about
20
hours.
B
Excuse
me,
Ickes
Wang
and
Peter
Shore,
who
are
two
of
the.
The
founders
of
this
field,
have
an
EDX
course
on
this,
and
theirs
is
about
60
hours
and
it
has
more
math
in
it.
I've
taken
a
look
at
some
of
that,
so
the
good
sequence
would
be
to
go
through
mine
and
then
to
go
through.
Theirs
would
be
a
reasonable
way
to
do
things.
You
are
everybody
who's
here
in
the
room
already
knows
about
the
existence
of
this
research
group.
B
If
you
are
not
on
the
mailing
list,
we
encourage
you
to
get
on
the
mailing
list.
There's
not
it's
not
very
high
traffic
level,
it's
just
in
small
bursts.
As
of
last
week,
there
were
236
people
on
the
list,
which
is
not
bad
and
Tracy
and
I
are
both
on
the
steering
committee
for
the
workshop
for
quantum
repeaters
and
networks
and
the
the
current
plan
is
for
the
next
one
of
those
to
be
September,
5
and
6
on
the
inland
sea
in
Japan.
B
Does
that
mean
no
final
questions?
Have
you
all
asked
all
of
your
questions?
Thank
you
all
for
being
here.
Thank
you
on
the
group
meeting
is
tomorrow,
12:20
I
think
maybe
it's
11:20
I'll
have
to
double-check.
It's
on
the
schedule
that
will
be
downstairs
in
Congress.
See
you
there.
Thank
you
all
for
sitting
through
two
hours
of
this.