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International Journal of Quantum Information

EFFECT OF DECOHERENCE ON FIDELITY IN TELEPORTATION OF ENTANGLED COHERENT STATES

Hari Prakash, Naresh Chandra, R. PRAKASH, SHIVANI

Published Oct 1, 2008• 15 citations
Publisher

Abstract

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.

DOI
10.1142/s0219749908004213

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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.
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.
A scheme of teleporting a superposition of coherent states |α> and |-α> using a 4-partite state, a beam splitter and two phase shifters was proposed by N. Ba An (Phys. Rev. A, 68, 022321, 2003). The author concluded that the probability for successful teleportation is only 1/4 in the limit |α|→∞ and 1/2 in the limit |α|→∞. In this paper it is shown that the author’s scheme can be altered slightly so as to obtain an almost perfect teleportation for an appreciable value of |α|2. We find the minimum assured fidelity i.e., the minimum fidelity for an arbitrarily chosen information state, which we write MAF in this paper, for different cases. We also discuss the effect of decoherence on teleportation fidelity. We find that if no photons are counted in both final outputs, MAF, is still nonzero except when there is no decoherence and the initial state (the state to be teleported) is even coherent state. For non-zero photon counts, MAF decreases with 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 initial state for low values of |α|2 only.
We consider a scheme of swapping between two pairs of non-orthogonal entangled coherent states with our suggested modification [H. Prakash, N. Chandra, R. Prakash and Shivani, Int. J. Mod. Phys. B 23(8) (2009) 2083] and discuss effect of decoherence on fidelity in swapping. We find that for odd photon counts, MAF (minimum of the fidelity for any arbitrary information) decreases with increase in |α|2 for low noise but in case of high noise, it increases, attains a maximum value and then decreases with |α|2. However, for nonzero even photon counts, the case is reversed. For this case, MAF decreases with increase in |α|2 for high noise but in case of low 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.
We study an entangled two-mode coherent state within the framework of2×2-dimensional Hilbert space. We investigate the problem of quantum teleportation ofa superposition coherent state via an entangled coherent channel. By three differentmeasures with the titles ``minimum assured fidelity (MASF)”, ``average teleportationfidelity” and ``optimal fidelity (f)” we study the quality of this kind of teleportation.Decoherence properties of the entangled coherent state due to channel losses areanalysed. For a symmetric noise channel, the degradation of optimal fidelity and degreeof entanglement are calculated. Also by two different measures with the titles``concurrence” and ``entanglement of formation” we study the amount of entanglementof a decohered quantum channel and discuss its details. We demonstrate thatentanglement of the decohered entangled coherent state is reduced but not throughlylost. Finally we find that the optimal fidelity of the decohered entangled coherent state ismore than the classical limit and the decohered entangled coherent state may be usefulfor quantum teleportation.
We consider the scheme for entanglement diversion proposed by Xin-Hua with our suggested modification (in press, issue 1 Jan 2009) and discuss the effect of decoherence on fidelity in such entanglement diversion. For odd photon counts, the fidelity 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. However, for nonzero even photon counts, the case is reversed. For this case, fidelity decreases with increase in |α|2 for high noise but in the case of low noise, it increases, attains a maximum value and then decreases with |α|2.
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 ${10}^{\ensuremath{-}4}$.