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Introduction to Quantum Teleportation

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For example, the following singlet state is entangled: or ... Bob have already shared an entangled state: Alice wants to give ... 'Path' entanglement was used. ... – PowerPoint PPT presentation

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Title: Introduction to Quantum Teleportation


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 Alices EPR photons
    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)
12
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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 Alices detectors
clicked, he can use RB to rotate his photons
polarization into an exact copy of Alices
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 0.853 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
(-)
27
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.
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