"Quantum Teleportation for Dogs"
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Transcript of "Quantum Teleportation for Dogs"
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