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Physical Science International Journal

Improving the Teleportation of Superposition of Entangled Coherent States

Shivani A. Kumar

Published Jan 10, 2014• 0 citations
Publisher

Abstract

I consider the teleportation of superposition of coherent states and using beam splitters and phase shifters. I propose some modifications which consist of writing the output state as a superposition of the vacuum state and nonzero even photon state, which allow for an almost perfect teleportation to be achieved for an appreciable mean number of photons.

DOI
10.9734/psij/2014/6307

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I consider the teleportation of superposition of coherent states and using beam splitters and phase shifters. I propose some modifications which consist of writing the output state as a superposition of the vacuum state and nonzero even photon state, which allow for an almost perfect teleportation to be achieved for an appreciable mean number of photons.
We consider the scheme proposed by Wang [Phys. Rev. A 64, 022302 (2001)] for teleporting bipartite entangled states using beam splitters and phase shifters. It is shown that the proposed scheme can be altered slightly so as to obtain an almost perfect teleportation for an appreciable mean number of photons. For mean number of photons equal to 2, the minimum of average fidelity which is the minimum of sum of the product of probability for occurrence of any case and the corresponding fidelity for an arbitrary bipartite entangled state is less than unity by a quantity of the order of ${10}^{\ensuremath{-}4}$.
We propose a nearly perfect optical scheme for the quantum teleportation of entangled coherent states using optical devices such as nonlinear Kerr media, beam splitters, phase shifters, and photon detectors. Different from those previous schemes, our scheme needs only ``yes'' or `no' measurements of the photon number of the related modes, i.e. nonzero- and zero-photon measurements, while in previous schemes one has to exactly identify the even or odd parity character of the photon numbers detected by detectors.
The present work proposes a scheme to teleport a tripartite coherent state using an unparalleled four-component state as a quantum channel. The scheme involves linear optical devices like beam splitters and phase shifters. It is shown that, even by taking an uncompromising quantum model, almost a complete teleportation can be achieved with an impressive number of photons. It is also shown that the teleportation fails only if zero photons are found in all the three output modes or zero in two output modes and a nonzero even/odd photon in one mode. However, the probability of getting these output modes is almost negligible.
A scheme of teleporting a superposition of coherent states |α⟩ and | − α⟩ using a beam splitter and two phase shifters was proposed by van Enk and Hirota (2001 Phys. Rev. A 64 022313). The authors concluded that the probability for successful teleportation is 1/2. In this paper, it is shown that the authors' scheme can be altered slightly so as to obtain an almost perfect teleportation for an appreciable value of |α| 2 . For |α| 2 = 5, the minimum of average fidelity, which is the minimum of the sum of the product of probability of occurrence of any case, and the corresponding fidelity is less than 1 by a quantity ∼10 −4 . We also discuss the effect of decoherence on teleportation fidelity. We find that if no photons are counted in both final outputs, the minimum assured fidelity is still non-zero except when there is no decoherence and the information is an even coherent state. For non-zero photon counts, minimum assured fidelity decreases with an increase in |α| 2 for low noise. For high noise, however, it increases, attains a maximum value and then decreases with |α| 2 . The average fidelity depends appreciably on the information for low values of |α| 2 only.
In a recent paper N. Ba An (Phys. Rev. A68, 022321 (2003)) proposed a scheme to teleport a single particle state, which is superposition of coherent states |α〉 and |-α〉 using a 4-partite state, a beam splitter, and phase shifters and concluded that the probability for successful teleportation is only 1/4 in the limit |α| → 0 and 1/2 in the limit |α| → ∞. In this paper, we modify this scheme and find that an almost perfect success can be achieved if |α|2 is appreciable. For example, for |α|2 = 5, the minimum of average fidelity for teleportation, which is the minimum of sum of the product of probability for occurrence of any case and the corresponding fidelity evaluated for an arbitrary chosen information state, is 0.9999.