Quantum teleportation
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Template:Cleanup-tone Quantum teleportation is a technique discussed in quantum information science to transfer a quantum state to an arbitrarily distant location using an entangled state and the transmission of some classical information.
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Quantum teleportation: the result
Now, imagine Alice's atom being in some complicated (excited) quantum state. Assume that we do not know this quantum state — and of course, we cannot find out by inspection (measurement). But what we can do is to teleport the quantum state to Bob's rubidium atom. After this operation, Bob's atom is exactly in the state that Alice's atom was before.
Now note that Bob's atom afterwards is indistinguishable from Alice's atom before. In a way, the two are the same — because it does not make sense to claim that two atoms are different only because they are at different locations. If Alice had gone to Bob and given him the atom we would have exactly the same physical situation.
But Alice and Bob were not required to meet. They only needed to share entanglement.
To see what this means, let us abstract to qubits. The atoms are now in states of the form α |ground state> + β |first excited state> <math> =: \alpha |0\rangle + \beta|1\rangle</math> (using bra-ket notation).
The method
As a prerequisite, Bob has produced two particles (or atoms, to stay with the concrete example) called I and II, which are maximally entangled, e.g. in the Bell state <math>|\Phi^+\rangle = \frac{1}{\sqrt{2}} (|0\rangle_I \otimes |0\rangle_{II} + |1\rangle_I \otimes |1\rangle_{II})</math>.
This means that the particles I and II are neither in the state |0> nor in |1> but rather in both simultaneously, and if you measure one of them you will find it to be |0> or |1> each with probability 1/2. But the other is then always in the same state, and this connects them by some "spooky action at a distance", as Einstein has put it.
Bob passed particle I to Alice (by moving it there through a quantum channel) and kept particle II. From now on, Alice can send a quantum state to Bob, whenever she wants (or Bob to Alice).
If Alice now has a particle which she wants to teleport to Bob, she does a so-called Bell measurement on the particle to be sent and on particle I. The Bell measurement (for details see the article on it) projects Alice's two particle into one of the four Bell states. The two measured particles are afterwards in a known entangled state, specified by the measurement result, and the particle to be sent has lost its former state. That state, however, is not gone: it was teleported to Bob's particle II due to the previously existing entanglement.
One problem remains: The state of Bob's particle might be "rotated". This depends on the outcome of Alice's measurement, and Alice has to tell Bob this outcome by using some classical (i.e. ordinary) communication channel and Bob will then apply a unitary operation (a so-called Pauli operator) onto his particle.2 Afterwards, he really has the desired state.
Entanglement swapping
If a state being teleported is itself entangled with another state, the entanglement is teleported with it. To illustrate: If Alice has a particle which is entangled with a particle owned by Carol, and she teleports it to Bob, then afterwards, Bob's particle is entangled with Carol's.
A more symmetric way to describe the situation is the following: Alice has one particle, Bob two, and Carol one. Alice's particle and Bob's first particle are entangled, and so are Bob's second and Carol's particle:
___
/ \
Alice-:-:-:-:-:-Bob1 -:- Bob2-:-:-:-:-:-Carol
\___/
Now, Bob performs a Bell measurement on his two particles, which projects them into a Bell state, i.e. they are now entangled. But, more spectacularly, Alice's and Carol's particles are now entangled as well, although the two never met:
Alice Bob2 -:- Bob1 Carol
| / \ |
\-:-:-:-:-:- -:-:-:-:-:-:-/
This effect allows (at least in theory) to build a quantum repeater (see there).
See also
References
- theoretical proposal:
- C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, & W. K. Wootters, Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels, Phys. Rev. Lett. 70 1895-1899 (1993) (this document online)
- G. Brassard, S Braunstein, R Cleve, Teleportation as a quantum computation, Physica D 120 43-47 (1998)
- G. Rigolin, Quantum teleportation of an arbitrary two qubit state and its relation to multipartite entanglement, Phys. Rev. A 71 032303 (2005) (this document online)
- A. Díaz-Caro, M. Gadella, A Discussion on the Teleportation Protocol for States of N Qubits, arXiv quant-ph/0505009 (2005) (this document online)
- first experiments with photons:
- D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, & A. Zeilinger, Experimental quantum teleportation, Nature 390, 6660, 575-579 (1997).
- D. Boschi, S. Branca, F. De Martini, L. Hardy, & S. Popescu, Experimental realization of teleporting an unknown pure quantum state via dual classical an Einstein-Podolsky-Rosen channels, Phys. Rev. Lett. 80, 6, 1121-1125 (1998);
- I. Marcikic, H. de Riedmatten, W. Tittel, H. Zbinden & N. Gisin: "Long-Distance Teleportation of Qubits at Telecommunication Wavelengths", Nature, Vol. 421, 509 (2003)
- R. Ursin et.al: Quantum Teleportation link across the Danube, Nature 430, 849 (2004)
- first experiments with atoms:
- M. Riebe, H. Häffner, C. F. Roos, W. Hänsel, J. Benhelm, G. P. T. Lancaster, T. W. Körber, C. Becher, F. Schmidt-Kaler, D. F. V. James, R. Blatt: Deterministic quantum teleportation with atoms, Nature 429, 734 - 737 (2004)
- M. D. Barrett, J. Chiaverini, T. Schaetz, J. Britton, W. M. Itano, J. D. Jost, E. Knill, C. Langer, D. Leibfried, R. Ozeri & D. J. Wineland: Deterministic quantum teleportation of atomic qubits, Nature 429, 737
External links
- signandsight.com:»Spooky action and beyond« - Interview with Prof. Dr. Anton Zeilinger about quantum teleportation. Date: 2006-02-16
- Quantum Teleportation at IBM
- (T.Bruce, PhD Can, Engineering)
- Physicists Succeed In Transferring Information Between Matter And Light
- Quantum Teleportation – The Fabricated Mystery
- Quantum telecloning: Captain Kirk's clone and the eavesdropper
- G.Olivares and L. Roa Decoherence assisting a measurement-driven quantum evolution process
Footnotes
1 with one technicality: If you swap two identical fermions their common wave function changes its sign. For this odd effect, see spin-statistics theorem.
2 As the measurement outcome will be one of the four Bell states, the message Alice has to send consists of 2 bits. Hence to teleport 1 qubit, we need 1 shared Bell pair (sometimes called 1 e-bit ("entangled bit")) and the transmission of 2 ordinary bits.
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