"Quantum Teleportation for Dogs"

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Information about "Quantum Teleportation for Dogs"
Education

Published on September 9, 2008

Author: orzelc

Source: slideshare.net

Description

A talk I gave at Boskone in 2008

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) Light speed close enough Fax Machine: 1) Scan document 2) Transmit Information 3) Print Copy Objections: 1) Not Instantaneous 2) Not Perfect Copy 3) Original Intact 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? WRONG Can’t measure both components Problem: Measurement determines state V?

Entangled States Need 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 States One dog, two states: Awake Asleep Two dogs, four states: Both Awake Both Asleep Awake Asleep Asleep Awake

Entangled Dogs Allow dogs to interact: Wake sleeping dog up to play Dogs are entangled : measure one, know other Both Awake Both Asleep Only two possible states:

Entangled Photons Same idea- photons with correlated states Equal chance of H or V (or any other angle) Measure one, know other Four possible states: I) |V 1 V 2 > + |H 1 H 2 > II) |V 1 V 2 > – |H 1 H 2 > III) |V 1 H 2 > + |H 1 V 2 > IV) |V 1 H 2 > – |H 1 V 2 >

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 |   > = |V 2 H 3 > – |H 2 V 3 > Start with arbitrary state Create two photons in entangled state IV Each take one

Step 2: Entangle EPS |   > = |V 2 H 3 > – |H 2 V 3 > |   > = a|V> + b|H> Make joint measurement of 1&2 DO NOT measure individually Same or different? One of four entangled states

Entangling Measurement |   > = a|V> + b|H> |   > = |V 2 H 3 > – |H 2 V 3 > Joint measurement entangles 1&2 Result of measurement determines state of photon 3 Don’t know state , but know relation 2&3 already entangled  1&3 entangled

Possible Outcomes Four possible results Each corresponds to rotation of original state Simple to undo I) |V 1 V 2 > + |H 1 H 2 > II) |V 1 V 2 > – |H 1 H 2 > III) |V 1 H 2 > + |H 1 V 2 > IV) |V 1 H 2 > – |H 1 V 2 > I) II) III) IV) -a|V>+b|H> b|V>+a|H> a|V>-b|H> -a|V>-b|H>

Step 3: Transmit EPS |   > = |V 2 H 3 > – |H 2 V 3 > III |   > = a|V> + b|H> III) Send result by classical means (phone, email, fax)

Step 4: Rotate EPS |   > = |V 2 H 3 > – |H 2 V 3 > III III) Four possible results Each corresponds to rotation of original state Rotate appropriately to get original state back

Experiment First Experiment: Innsbruck 1997 50 cm 2004, Vienna: 600 m (across Danube) Analysis Transmission Trigger Entangling Measurement 1 2 3 4

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: Send atomic states Entangle atoms w/photons, send photons Transfer states between atoms (Copenhagen 2006) 2) “Quantum Internet” Network quantum computers together 3) Teleporting brain states Quantum consciousness (Penrose, etc.)?

Send atomic states

Entangle atoms w/photons, send photons

Transfer states between atoms

(Copenhagen 2006)

Summary Quantum measurement prevents state copying Entanglement allows action at a distance Use entangled states to transmit exact state Gets around measurement problem Caveats: 1) Not FTL 2) Not Cloning Still a long way from Star Trek …

The End

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