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QUANTUM PHYSICS: ON ATOM QUANTUM TELEPORTATION

Notes by ScienceWeek:

Quantum teleportation is the transmission and reconstruction over arbitrary distances of the state of a quantum system, an effect first suggested by Bennett et al in 1993 (Phys. Rev. Lett. 70:1895). The achievement of the effect depends on the phenomenon of entanglement, an essential feature of quantum mechanics. Entanglement is unique to quantum mechanics, and involves a relationship (a "superposition of states") between the possible quantum states of two entities such that when the possible states of one entity collapse to a single state as a result of suddenly imposed boundary conditions, a similar and related collapse occurs in the possible states of the entangled entity no matter where or how far away the entangled entity is located.

The following points are made by M. Riebe et al (Nature 2004 429:734):

1) Teleportation of a quantum state encompasses the complete transfer of information from one particle to another. The complete specification of the quantum state of a system generally requires an infinite amount of information, even for simple two-level systems (qubits). Moreover, the principles of quantum mechanics dictate that any measurement on a system immediately alters its state, while yielding at most one bit of information. The transfer of a state from one system to another (by performing measurements on the first and operations on the second) might therefore appear impossible. However, it has been shown(1) that the entangling properties of quantum mechanics, in combination with classical communication, allow quantum-state teleportation to be performed. Teleportation using pairs of entangled photons has been demonstrated(2-5), but such techniques are probabilistic, requiring post-selection of measured photons.

2) Teleportation of a state from a source qubit to a target qubit requires three qubits: the sender's source qubit and an ancillary qubit that is maximally entangled with the receiver's target qubit, providing the strong quantum correlation. Once these states have been prepared, a quantum mechanical measurement is performed jointly on the source qubit and the ancilla qubit (specifically, a Bell-state measurement, which projects the two qubits onto a basis of maximally entangled states). In this process, the two qubits are projected onto one of four equally likely outcomes. At the same time, the non-local properties of quantum mechanics cause the target qubit to be projected onto one of four corresponding states, each related to the original state of the source qubit, even though no measurement was performed on this qubit. Knowledge of the result of the source-ancilla measurement allows one to choose a simple a priori operation to be carried out on the target qubit, resulting in reconstruction of the original quantum state.

3) Because each of the four results on the source-ancilla measurement are equally likely, regardless of the nature of the teleported state, no information about the state is obtained (thus the no-cloning theorem is not violated). Further, as classical communication of the measurement outcome is required to complete the state reconstruction, a state cannot be teleported faster than the speed of light. Teleportation does demonstrate a number of fascinating fundamental properties of quantum theory, in particular the non-local property of entangled states, which allows the projective measurement of the source-ancilla pair to create a definite pure state in the target qubit. Furthermore, teleportation has considerable implications for the nascent technology of quantum information processing. Besides being a compelling benchmark algorithm for a three-qubit quantum computer, teleportation is a possible primitive for large-scale devices.

4) In summary: The authors report deterministic quantum-state teleportation between a pair of trapped calcium ions. Following closely the original proposal(1), the authors create a highly entangled pair of ions and perform a complete Bell-state measurement involving one ion from this pair and a third source ion. State reconstruction conditioned on this measurement is then performed on the other half of the entangled pair. The measured fidelity is 75%, demonstrating unequivocally the quantum nature of the process.

References (abridged):

1. Bennett, C. H. et al. Teleporting an unknown quantum state via dual classical and EPR channels. Phys. Rev. Lett. 70, 1895-1899 (1993)

2. Bouwmeester, D. et al. Experimental quantum teleportation. Nature 390, 575-579 (1997)

3. Boschi, D., Branca, S., DeMartini, F., Hardy, L. & Popescu, S. Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 80, 1121-1125 (1998)

4. Pan, J.-W., Daniell, M., Gasparoni, S., Weihs, G. & Zeilinger, A. Experimental demonstration of four-photon entanglement and high-fidelity teleportation. Phys. Rev. Lett. 86, 4435-4438 (2001)

5. Marcikic, I., de Riedmatten, H., Tittel, W., Zbinden, H. & Gisin, N. Long-distance teleportation of qubits at telecommunication wavelengths. Nature 421, 509-513 (2003)

Nature http://www.nature.com/nature

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Related Material:

ON QUANTUM TELEPORTATION AND ENTANGLEMENT SWAPPING

Notes by ScienceWeek:

In general, a "Hilbert space" is a linear vector space that can have an infinite number of dimensions, the concept important because in quantum mechanics the state of a system is represented by a vector in Hilbert space. The dimension of the Hilbert space is not related to the physical dimension of the system. The concept is named after the mathematician David Hilbert (1862-1943).

The following points are made by D.W. Berry and B.C. Sanders {New Journal of Physics 2002 4:8):

1) Quantum teleportation enables disembodied transport of the state of a system to a distant system through (i) a shared entanglement resource, (ii) a classical communication channel between the sender and receiver [1] and (iii) an experimentally established isomorphism between the Hilbert spaces of the sender and receiver [2]. Quantum teleportation is significant in several areas, including transmission of quantum states in noisy environments [1], sharing states in distributed quantum networks [3] and implementation of quantum computation using resources prepared offline [4,5]. Teleportation was initially proposed for discrete-variable systems, where the state to be teleported has finite-N levels [1], and a continuous-variable version has been adapted for squeezed light experiments. The authors discuss quantum teleportation of a quantum state in an arbitrary but finite N-dimensional Hilbert space , realized physically as a spin system, thereby generalizing the recent spin quantum teleportation proposal by Kuzmich and Polzik (Phys. Rev. Lett. 2000 85:5639), which is only valid in the infinite-N limit.

2) "Entanglement swapping" is closely related to quantum teleportation. Whereas quantum teleportation enables the state of a system (e.g. a particle or collection of particles) to be teleported to an independent physical system via classical communication channels and a shared entanglement resource, the purpose of entanglement swapping is to instill entanglement between systems that hitherto shared no entanglement. An entanglement resource is required for entanglement swapping to occur; indeed the nomenclature "entanglement swapping" describes the transfer of entanglement from a priori entangled systems to a priori separable systems.

3) A connection between entanglement swapping and quantum teleportation can be seen as follows. Consider quantum teleportation of the state of one particle, which is initially entangled with a second particle, but the state of the second particle does not undergo quantum teleportation. In perfect quantum teleportation, the state of the first particle is faithfully transferred to a third particle that was initially independent of the first two particles. Thus, subsequent to the quantum teleportation, the second and third particles are entangled, perfectly replacing the a priori entanglement of the first and second particles. The entanglement resource inherent in quantum teleportation devices enables this entanglement swapping to occur; thus, equivalence between optimal entanglement resources for quantum teleportation and entanglement swapping might be expected, but the authors demonstrate that the optimal entanglement resources differ between quantum teleportation and entanglement swapping for finite-N spin systems.

References (abridged):

1. Bennett C H, Brassard G, Crepeau C, Jozsa R, Peres A and Wootters W K 1993 Phys. Rev. Lett. 70:1895

2. van Enk S J 2001 J. Mod. Opt. 48:2049

3. Cirac J I, Ekert A K, Huelga S F and Macchiavello C 1999 Phys. Rev. A 59:4249

4. Gottesman D and Chuang I L 1999 Nature 402:390

5. Knill E, Laflamme R and Milburn G J 2001 Nature 409:46

New Journal of Physics http://www.iop.org/EJ/njp

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