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arXiv:1107.2533

Increasing Average Fidelity by Using Non-Maximally Entangled Resource in Teleportation of Superposed Coherent States

Hari Prakash, Manoj Kumar Mishra

Published Jul 13, 2011• 3 citations
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Abstract

We consider the problem of teleporting superposed coherent state using non-maximally entangled coherent state as quantum channel and study the effect of entanglement over quality of teleportation. We show that if maximally entangled coherent state (MECS) used by Van Enk and Hirota [Phys. Rev. A 64, 022313 (2001)] and by H Prakash et al. [Phys. Rev. A 75, 044305 (2007)] is replaced by a particular non-maximally entangled coherent state (NMECS), average fidelity of quantum teleportation increases appreciably at small coherent amplitudes. Since it is very challenging to produce superposed coherent states of large coherent amplitudes, the particular NMECS appear to be a good quantum channel for teleportation at small coherent amplitudes for practical implementation.

DOI
10.48550/arxiv.1107.2533

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We consider the problem of teleporting superposed coherent state using non-maximally entangled coherent state as quantum channel and study the effect of entanglement over quality of teleportation. We show that if maximally entangled coherent state (MECS) used by Van Enk and Hirota [Phys. Rev. A 64, 022313 (2001)] and by H Prakash et al. [Phys. Rev. A 75, 044305 (2007)] is replaced by a particular non-maximally entangled coherent state (NMECS), average fidelity of quantum teleportation increases appreciably at small coherent amplitudes. Since it is very challenging to produce superposed coherent states of large coherent amplitudes, the particular NMECS appear to be a good quantum channel for teleportation at small coherent amplitudes for practical implementation.
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.
Quantum Teleportation of N qubits with perfect fidelity using maximally entangled states is explained. It is shown that non-maximally entangled states are used the minimum assured fidelity decreases. It is explained how the success 1/2 of teleportation of a superposition of even and odd coherent states suggested by Van Enk and Hirota was modified by Prakash, Chandra, Prakash and Shivani. It is also shown that the decrease in entanglement may sometimes even result in increase in fidelity. so as to make the success nearly 1. It is also explained how decoherence can be taken into account and how such schemes can be applied to similar phenomena of entanglement diversion and entanglement swapping.
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.
The effects of amplitude damping in quantum noise channels on average fidelity of quantum teleportation are analyzed in Bloch sphere representation for every stage of teleportation. When the quantum channels are varied from maximally entangled states to non-maximally entangled states, it is found that the effects of noise channels on the fidelity are nearly equivalent to each other for strong quantum noise. The degree of damage on the fidelity of non-maximally entangled channels is smaller than that of maximally entangled channels. The average fidelity of values larger than 2/3 may be one representation indirectly showing how much the unavoidable quantum noise is.
We investigate the problem of teleportation of a superposition coherent state via a nonmaximally entangled coherent channel. Two strategies are considered to complete the task. The first one uses entanglement concentration to purify the channel to a maximally entangled one. The second one teleports the state through the nonmaximally entangled coherent channel directly. We find that the probabilities of successful teleportation for the two strategies depend on the amplitudes of the coherent states, and the mean fidelity of teleportation using the first strategy is always less than that using the second strategy.
We consider the scheme proposed by Wang [Phys. Rev. A64 (2001) 022302] for teleporting bipartite entangled states, which is a superposition of coherent states |α,α〉 and |-α,-α〉, with our suggested modification [Phys. Rev. A75 (2007) 044305] and discuss the effect of decoherence on teleportation fidelity. We find that if no photons are counted in both final outputs, the minimum assured fidelity (MAF), which is the minimum of the fidelity for any arbitrary information), is still nonzero except for the case when there is no decoherence and the information is in even coherent state. For non-zero photon counts, MAF decreases with increase in |α|2 for low noise but in the case of high noise, it increases, attains a maximum value and then decreases with |α|2. We discuss the variation of average fidelity with |α|2 and show that it depends appreciably on the information for low values of |α|2 only.