The document discusses quantum teleportation as a method for transmitting the exact quantum state of a particle to a distant location. It involves: 1) Creating an entangled pair of particles to use as a resource. 2) Performing a joint measurement on the particle with the state to transmit and one particle from the entangled pair, entangling them. 3) Transmitting the measurement result classically to allow reconstructing the original state in the other particle from the entangled pair.

1. Quantum Teleportation For Dogs

2. “ I have a plan…”

3. “ Pleeeease???”

4. “ We don’t like those dogs…”

5. “ I guess it’s back to plan A…”

6. Teleportation (Ideal)

7. 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

8. Quantum Teleportation Goal: Transmit quantum state Get exact copy in new location Problem: Quantum Measurement

9. 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

10. 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?

11. 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”

12. Dog States One dog, two states: Awake Asleep Two dogs, four states: Both Awake Both Asleep Awake Asleep Asleep Awake

13. 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:

14. 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 >

15. 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

16. 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

17. 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

18. 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

19. 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>

20. 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)

21. 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

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

23. 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

25. 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 …

26. The End