1. Introduction to Quantum Teleportation
By Dumb Scientist
First created: May 15, 2007
Last modified: October 29, 2008
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2. Problems with Teleportation
The uncertainty principle forbids simultaneous measurements of non-commuting observables.
Consider trying to measure a simple system like the polarization state of a single photon:
Trying to measure  and  simply collapses the state, giving only 1 bit of information!

3. Problems with Teleportation
Only by performing repeated measurements on copies of the same state can  and  be determined with any accuracy.
This method cannot be applied to teleportation of unknown states because the “no-cloning” theorem1 forbids copying quantum states.
1 W.K. Wootters and W.H. Zurek, Nature 299, 802 (1982).

4. Quantum Entanglement
Two particles are said to be “entangled” if measurements on one particle are correlated with measurements on the other particle. For example, the following singlet state is entangled:
Notice that measuring particle 1 puts particle 2 into a definite state: or

5. The “BBCJPW” Protocol
In 1993, a method of teleporting a two-state quantum system was published by six co-authors, collectively known as BBCJPW2.
Suppose Alice and Bob have already shared an entangled state:
Alice wants to give Bob the state
2 C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Pere and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).

6. BBCJPW Protocol
Alice then measures particles 2 and 3 using the following basis:

7. BBCJPW Protocol
Alice then measures particles 2 and 3 using the following basis:

8. BBCJPW Protocol
Alice needs to tell Bob the result of her measurement (2 classical bits), which limits teleportation to light speed.
No energy or matter is transferred.
The no-cloning theorem is not violated because the state |3i has been destroyed.

9. Boschi Teleportation Experiment
In 1998, a team led by D. Boschi demonstrated3 quantum teleportation of polarization states of photons.
Key differences from the BBCJPW protocol:
“Path” entanglement was used.
A total of 2 photons were used- the state to be teleported is “imprinted” on Alice’s EPR photon’s polarization state.
3 D. Boschi, et al., Phys. Rev. Lett. 80, 1121 (1998).

10. Boschi Teleportation Experiment
(Diagram adapted from [3])

11. Boschi Teleportation Experiment
(Diagram adapted from [3])

15. Alice measures photon #1 in this basis:

16. Alice measures photon #1 in this basis:
Half-wave plate in path b1 rotates polarization by 90º:

17. Alice measures photon #1 in this basis:
Half-wave plate in path b1 rotates polarization by 90º:

18. Alice measures photon #1 in this basis:
(+)
Half-wave plate in path b1 rotates polarization by 90º:
(-)

19. Alice measures photon #1 in this basis:
(+)
Half-wave plate in path b1 rotates polarization by 90º:
(-)

20. Alice measures photon #1 in this basis:
(+)
Half-wave plate in path b1 rotates polarization by 90º:
(-)

21. (+)
(-)

22. (+)
(-)

23. How do we verify that teleportation was successful?
(+)
If Bob is told which of Alice’s detectors clicked, he can use RB to rotate his photon’s polarization into an exact copy of Alice’s polarization state.
(-)

24. How do we verify that teleportation was successful?
Bob sets RB so it sends the teleported state to DB to measure a coincidence rate called
(+)
(-)

25. How do we verify that teleportation was successful?
Bob sets RB so it sends the teleported state to DB to measure a coincidence rate called
(+)
Bob sets RB so it sends the teleported state away from DB to measure a coincidence rate called
(-)

26. How do we verify that teleportation was successful?
Result: S = ± 0.012
Bob sets RB so it sends the teleported state to DB to measure a coincidence rate called
(+)
The classical limit on “S” (without using entanglement) is Thus, these results break the classical limit by 8 standard deviations.
Bob sets RB so it sends the teleported state away from DB to measure a coincidence rate called
(-)

27. Conclusion
Experiments have demonstrated teleportation of polarization, atomic energy levels and squeezed states of light.
Can’t claim that a single photon has been teleported in its entirety because we’ve ignored the photon’s spatial states, frequency and k-vector.
Scaling up teleportation to handle macroscopic objects presents enormous challenges.
In the near term, quantum teleportation is useful for linking quantum computers and providing truly secure communication.