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Journal of Optics B Quantum and Semiclassical Optics

Teleportation of entangled states

В. Н. Горбачев, A. I. Zhiliba, Andrew I. Trubilko

Published Jan 25, 2001• 26 citations
Publisher

Abstract

Teleportation of some pure entangled states of discrete and continuous variables is considered using a multi-particle quantum channel; particularly a Greenberger-Horne-Zeilinger channel. Both the protocols we have found for the discrete and continuous versions have identical features due to the properties of the quantum channel. In this way some entangled states can be teleported perfectly; a non-Bell-state measurement is needed in contrast to the one-by-one protocol where an unknown state can be recovered by all receivers only. For teleportation of continuous variables an optical implementation using squeezed light states is discussed.

DOI
10.1088/1464-4266/3/1/355

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Teleportation of some pure entangled states of discrete and continuous variables is considered using a multi-particle quantum channel; particularly a Greenberger-Horne-Zeilinger channel. Both the protocols we have found for the discrete and continuous versions have identical features due to the properties of the quantum channel. In this way some entangled states can be teleported perfectly; a non-Bell-state measurement is needed in contrast to the one-by-one protocol where an unknown state can be recovered by all receivers only. For teleportation of continuous variables an optical implementation using squeezed light states is discussed.
The teleportation of a two-particle entangled state, using a Greenberger-Horne-Zeilinger triplet, for continuous variables is studied. The basis for joint three-particle measurements is found, where the vectors describe the states in which only two of three particles are entangled. It represents the measurement of the momentum of one particle and the difference of coordinates and the sum of momenta of the two other particles. An optical realization of this scheme is presented, which uses squeezed states of light and reduces the measurement of momentum and coordinate to the detection of quadrature operators of the electromagnetic field.
Quantum teleportation protocols of continuous variable (CV) Greeberger–Horne–Zeilinger (GHZ) and Einstein–Podolsky–Rosen (EPR) entangled states are proposed, and are generalized to teleportation of arbitrary multimode GHZ entangled states described by Van Loock and Braunstein (2000 Phys. Rev. Lett. 84 3482). Each mode of a multimode entangled state is teleported using a CV EPR entangled pair and classical communication. The analytical expression of fidelity for the multimode Gaussian states which evaluates the teleportation quality is presented. The analytical results show that the fidelity is a function of both the squeezing parameter r, which characterizes the multimode entangled state to be teleported, and the channel parameter p, which characterizes the EPR pairs shared by Alice and Bob. The fidelity increases with increasing p, but decreases with increasing r, i.e., it is more difficult to teleport the more perfect multimode entangled states. The entanglement degree of the teleported multimode entangled states increases with increasing both r and p. In addition, the fact is proved that our teleportation protocol of EPR entangled states using parallel EPR pairs as quantum channels is the best case of the protocol using four-mode entangled states (Adhikari et al 2008 Phys. Rev. A 77 012337).
The wave-particle duality of light has led to two different encodings of optical quantum information. One approach, referred to as the discrete-variable (DV) one, relies on finite dimensional quantum systems, while the other one, referred to as the continuous-variable (CV) one, is based on wave-like states belonging to an infinite dimensional Hilbert space. These two encodings have historically been separated, but recently, new hybrid protocols which aim at combining the advantages of the two encodings have emerged [1] . In that prospect our recent demonstration of the measurement-induced generation of hybrid entanglement between discrete- and continuous-variable quantum states [2] , [3] , located at distant places and connected by a lossy channel, has opened the way to the implementation of hybrid protocols and heterogeneous quantum networks. Following the first protocols based on this resource, such as the remote preparation of continuous-variable qubits [4] , or a violation of an Einstein-Podolsky-Rosen steering inequality [5] , we will here report our latest experimental results on entanglement swapping and quantum teleportation protocols using hybrid entangled states based on different encodings [6] .