Introduction to Quantum Teleportation

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Introduction to Quantum Teleportation

• By Dumb Scientist
• First created May 15, 2007
• Last modified October 29, 2008

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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!

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

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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 Alices EPR photons
  polarization state.

3 D. Boschi, et al., Phys. Rev. Lett. 80, 1121
(1998).
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Boschi Teleportation Experiment
(Diagram adapted from 3)
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Boschi Teleportation Experiment
(Diagram adapted from 3)
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Alice measures photon 1 in this basis
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Alice measures photon 1 in this basis
Half-wave plate in path b1 rotates polarization
by 90º
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Alice measures photon 1 in this basis
Half-wave plate in path b1 rotates polarization
by 90º
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Alice measures photon 1 in this basis
()
Half-wave plate in path b1 rotates polarization
by 90º
(-)
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Alice measures photon 1 in this basis
()
Half-wave plate in path b1 rotates polarization
by 90º
(-)
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Alice measures photon 1 in this basis
()
Half-wave plate in path b1 rotates polarization
by 90º
(-)
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()
(-)
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()
(-)
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How do we verify that teleportation was
successful?
()
If Bob is told which of Alices detectors
clicked, he can use RB to rotate his photons
polarization into an exact copy of Alices
polarization state.
(-)
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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
()
(-)
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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
(-)
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How do we verify that teleportation was
successful?
Result S 0.853 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 0.75. 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
(-)
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Conclusion

• Experiments have demonstrated teleportation of
  polarization, atomic energy levels and squeezed
  states of light.
• Cant claim that a single photon has been
  teleported in its entirety because weve ignored
  the photons 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.