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Acta Physica Sinica

Fidelity of the scheme of continunous variables quantum teleportation via minimum-correlation mixed quantum states

Yun‐Jie Xia, Guanghui Wang, Shao-Jiang Du, (1)济宁师范专科学校物理系，曲阜 273155; (2)曲阜师范大学物理工程学院，曲阜 273165

Published Jan 1, 2007• 6 citations
Publisher

Abstract

Based on the proposal of Braunstein and Kimble，we studied the continuous variables quantum teleportation via minimum-correlation mixed state. The results show that the mixed entangled state as a generalized type of Einstein-Podolsky-Rosen entangled states is a good quantum channel. As an example，we analyzed in detail teleporting a coherent state by means of this channel. When the parameters of minimum-correlation mixed state are chosen properly，the fidelity will almost reach to unity. The minimum-correlation mixed state as a quantum channel is better than the two-mode squeezed vacuum state.

DOI
10.7498/aps.56.4331

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Based on the proposal of Braunstein and Kimble，we studied the continuous variables quantum teleportation via minimum-correlation mixed state. The results show that the mixed entangled state as a generalized type of Einstein-Podolsky-Rosen entangled states is a good quantum channel. As an example，we analyzed in detail teleporting a coherent state by means of this channel. When the parameters of minimum-correlation mixed state are chosen properly，the fidelity will almost reach to unity. The minimum-correlation mixed state as a quantum channel is better than the two-mode squeezed vacuum state.
ABSTRACT We propose a setup for teleportation of continuous quantum variables which is optimized for teleportation ofsqueezed coherent states. Our scheme is a modified version of the original setup proposed by Braunstein andKimble [Phys. Rev. Lett. 80, 869, 1998] and it involves an unbalanced beam splitter on the sender's side and asingle mode squeezer on receiver's side. We show that the quality of the teleportation can be evaluated by meansof a fidelity of entanglement swapping and we prove that our modified setup and the original Braunstein-Kimblesetup are equivalent with respect to this fidelity measure.Keywords: Quantum teleportation, squeezed states, completely positive maps, fidelity 1. INTRODUCTION Quantum teleportation, a disembodied transfer of a quantum state between two distant parties, is perhaps themost remarkable and exciting development in the rapidly growing field of quantum information processing. Intheir seminal paper, Bennett et al.1 proposed a protocol for teleportation of a single qubit from the sender Aliceto the receiver Bob. The information about the teleported state is sent to Bob via dual classical and quantumEPR channels. The latter is established by a maximally entangled state shared by Alice and Bob.Recently, there has been much interest in quantum information processing with continuous quantum van-ables. Here, the focus is on systems with infinite dimensional Hubert spaces such as quantized electromagneticfield. Teleportation of continuous quantum variables was first considered by Vaidman,2 and an experimentallyfeasible setup was suggested by Braunstein and Kimble.3 Subsequent experiment4 demonstrated that theteleportation of a single mode of optical field is fully within the reach of current technology. Since then, manyauthors discussed various aspects of the teleportation,5'° including fidelity of teleportation of various quantumstates and influence of losses on the degradation of the quantum channel.Besides teleportation, many other protocols developed originally in the framework of discrete quantum van-ables, have been successfully formulated also for continuous variables. These include quantum cloning,11'3quantum
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).