Quantum Teleportation

For Dogs

“I have a plan…”

“Pleeeease???”

“We don’t like those dogs…”

“I guess it’s back to plan A…”

Teleportation (Ideal)

Teleportation (Classical Reality)Fax Machine:

1) Scan document

2) Transmit Information

3) Print Copy

Objections:1) Not Instantaneous

2) Not Perfect Copy

3) Original Intact

Light speed close enough

Just engineering problems: better scanner shredder

Quantum Teleportation

Goal: Transmit quantum state Get exact copy in new location

Problem: Quantum Measurement

Polarized Photons

Polarization at some angle

Some probability of either |H> or |V>

Describe as combination of horizontal and vertical

|> = a|V> + b|H>

a

b

a-b

Teleporting Photons

Want to send photon at arbitrary angle

Just measure H & V, send those values, right?

WRONGProblem: Measurement determines state

V?

Can’t measure both components

Entangled StatesNeed clever trick to teleport photon state

Use “entangled states” as a resource

Two systems, states depend on one another

Measure one, know other

Instantaneous, non-local

“Spooky action at a distance”

Dog StatesOne dog, two states:

Awake Asleep

Two dogs, four states:

BothAwake

BothAsleep

AwakeAsleep

AsleepAwake

Entangled DogsAllow dogs to interact:

Wake sleeping dog up to play

Both Awake Both Asleep

Only two possible states:

Dogs are entangled: measure one, know other

Entangled PhotonsSame idea- photons with correlated states

Four possible states:

I) |V1V2 > + |H1H2 >II) |V1V2 > – |H1H2 >III) |V1H2 > + |H1V2>IV) |V1H2 > – |H1V2 >

Equal chance of H or V (or any other angle)

Measure one, know other

Quantum Teleportation

Four-step process:

1) Exchange entangled pair

2) Entangling measurement

3) Classical transmission

4) Final rotation

End with exact state in new location

Step 1: Exchange

|> = a|V> + b|H>

EPS

|> = |V2H3> – |H2V3>

Start with arbitrary state

Create two photons in entangled state IV

Each take one

Step 2: Entangle

EPS

|> = |V2H3> – |H2V3>

|> = a|V> + b|H>

Make joint measurement of 1&2DO NOT measure individually

Same or different?One of four entangled states

Entangling Measurement

|> = a|V> + b|H>

|> = |V2H3> – |H2V3>

Joint measurement entangles 1&2

2&3 already entangled

1&3 entangled

Result of measurement determines state of photon 3

Don’t know state, but know relation

Possible OutcomesFour possible results

Each corresponds to rotation of original state

Simple to undo

I) |V1V2 > + |H1H2 >II) |V1V2 > – |H1H2 >III) |V1H2 > + |H1V2>IV) |V1H2 > – |H1V2 >

I) II) III) IV)

-a|V>+b|H> b|V>+a|H> a|V>-b|H> -a|V>-b|H>

Step 3: Transmit

EPS

|> = |V2H3> – |H2V3>

III|> = a|V> + b|H>

III)

Send result by classical means

(phone, email, fax)

Step 4: Rotate

EPS

|> = |V2H3> – |H2V3>

III

III)

Four possible results

Each corresponds to rotation of original state

Rotate appropriately to get original state back

Experiment

Analysis

Transmission

Trigger

Entangling Measurement

1 2

34

First Experiment:Innsbruck 199750 cm

2004, Vienna:600 m (across Danube)

Comparison

How does this stack up?

2) NOT FTL– Teleportation not complete w/o classical transmission

3) Original is lost– entangling measurement changes state of 1

1) Perfect copy of original state, no matter what it is

Why Bother?Seems like a lot of work just to send one photon…

Applications:

1) Send atomic statesEntangle atoms w/photons, send photonsTransfer states between atoms(Copenhagen 2006)

2) “Quantum Internet”Network quantum computers together

3) Teleporting brain statesQuantum consciousness (Penrose, etc.)?

Summary

Quantum measurement prevents state copying

Entanglement allows action at a distance

Use entangled states to transmit exact stateGets around measurement problem

Caveats:

1) Not FTL 2) Not Cloning

Still a long way from Star Trek…

The End