Title: Introduction to Quantum Teleportation
1Introduction to Quantum Teleportation
- By Dumb Scientist
- First created May 15, 2007
- Last modified October 29, 2008
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2Problems 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!
3Problems 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).
4Quantum 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
5The 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).
6BBCJPW Protocol
Alice then measures particles 2 and 3 using the
following basis
7BBCJPW Protocol
Alice then measures particles 2 and 3 using the
following basis
8BBCJPW 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.
9Boschi 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).
10Boschi Teleportation Experiment
(Diagram adapted from 3)
11Boschi Teleportation Experiment
(Diagram adapted from 3)
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15Alice measures photon 1 in this basis
16Alice measures photon 1 in this basis
Half-wave plate in path b1 rotates polarization
by 90º
17Alice measures photon 1 in this basis
Half-wave plate in path b1 rotates polarization
by 90º
18Alice measures photon 1 in this basis
()
Half-wave plate in path b1 rotates polarization
by 90º
(-)
19Alice measures photon 1 in this basis
()
Half-wave plate in path b1 rotates polarization
by 90º
(-)
20Alice measures photon 1 in this basis
()
Half-wave plate in path b1 rotates polarization
by 90º
(-)
21()
(-)
22()
(-)
23How 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.
(-)
24How do we verify that teleportation was
successful?
Bob sets RB so it sends the teleported state to
DB to measure a coincidence rate called
()
(-)
25How 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
(-)
26How 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
(-)
27Conclusion
- 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.