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Physica Scripta

Entanglement and nonlocality of photon-added entangled coherent states and quantum probabilistic teleportation

Jian-Song Zhang, Jing‐Bo Xu

Published Feb 1, 2009• 20 citations
Publisher

Abstract

We introduce photon-added entangled coherent states (unnormalized) : and investigate the entanglement by employing the entropy of entanglement. Then, we propose a scheme of probabilistic teleportation via photon-added entangled coherent states. It is shown that the mean fidelity of the scheme can be increased by exciting entangled coherent states in the case of nonmaximally entangled quantum channel. The violation of the Clauser?Horne?Shimony?Holt inequality for photon-added entangled coherent states is also examined.

DOI
10.1088/0031-8949/79/02/025008

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We introduce photon-added entangled coherent states (unnormalized) : and investigate the entanglement by employing the entropy of entanglement. Then, we propose a scheme of probabilistic teleportation via photon-added entangled coherent states. It is shown that the mean fidelity of the scheme can be increased by exciting entangled coherent states in the case of nonmaximally entangled quantum channel. The violation of the Clauser?Horne?Shimony?Holt inequality for photon-added entangled coherent states is also examined.
We consider the problem of teleporting superposed coherent state using nonmaximally entangled coherent state (NMECS) as quantum channel and study the effect of entanglement on the quality of teleportation. Based on the amount of entanglement shared between the sender and the receiver, we propose two unitary operation strategies to be adopted by the receiver to recover replica of information state with as large a fidelity as possible, and analyzed the behavior of minimum average fidelity (MAF) and mean fidelity (MF) with respect to entanglement. It is fascinatingly found that if the maximally entangled coherent state used in previously proposed schemes is replaced by a particular NMECS, MAF of quantum teleportation increases appreciably at small coherent amplitudes. For coherent amplitudes with |α|2≤0.5, MECS gives higher MF, while for |α|2≥0.5, NMECS gives higher MF.
The Bell--Clauser-Horne-Shimony-Holt (BCHSH) inequality (in terms of correlation functions) of two qutrits is studied in detail by employing tritter measurements. A uniform formula for the maximum value of this inequality for tritter measurements is obtained. Based on this formula, we show that nonmaximally entangled states violate the BCHSH inequality more strongly than the maximally entangled one. This result is consistent with what was obtained by Ac\'{\i}n et al. [Phys. Rev. A 65,65,65, 052325 (2002)] using the Bell--Clauser-Horne inequality (in terms of probabilities).
Clauser-Horne-Shimony-Holt inequality for bipartite systems of four dimensions is studied in detail by employing the unbiased eight-port beam splitters measurements. The uniform formulas for the maximum and minimum values of this inequality for such measurements are obtained. Based on these formulas, we show that an optimal nonmaximally entangled state is about 66%6 more resistant to noise than the maximally entangled one. We also give the optimal state and the optimal angles which are important for experimental realization.
We propose a scheme for teleportation of an entangled coherent state through bipartite entangled quantum channels. We study the problem in both coherent state picture and orthogonal basis picture composed of coherent states, and find that in the coherent state picture teleportation can be implemented using only linear elements, but the probability of success is less than 1/2, while in the orthogonal basis picture the probability of successful teleportation reaches 1 as long as the four Bell states can be discriminated.