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International Journal of Modern Physics B

ENTANGLEMENT DIVERSION BETWEEN TWO PAIRS OF ENTANGLED COHERENT STATES: FIDELITY AND DECOHERENCE

Hari Prakash, Naresh Chandra, R. PRAKASH, Shivani A. Kumar

Published Feb 10, 2009• 13 citations
Publisher

Abstract

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.

DOI
10.1142/s0217979209049930

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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 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 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.
In the present paper, we will review the methods to produce superposition of entangled coherent state using polarizing beam splitter and Kerr non linearity. These coherent states have many attractive features and can be used in various schemes. Entanglement, refers to the superposition of a multiparticle system and explains a new type of correlations between any two subsystems of the quantum system, which is not existing in the classical physics. The present paper deals with the use of these states in quantum teleportation, entanglement diversion and entanglement swapping schemes. Entanglement diversion and entanglement-swapping refers to a scheme which may entangle those particles which had never interacted before. In the swapping scheme, two pairs of entangled state are taken. One particle from each pair is subjected to a Bell-state-measurement. This would result in projection of the other two outgoing particles in an entangled pair. Quantum Teleportation of two mode and three modes states is also studied with perfect fidelity. Minimum assured fidelity which is defined as the minimum of the fidelity for any unknown quantum information of the states is also discussed. It is also shown how the success rate of teleportation of a superposition of odd and even coherent states can be increased from 50% to almost 100%. The scheme suggested by van Enk and Hirota was modified by Prakash, Chandra, Prakash and Shivani in 2007. We find that an almost teleportation, diversion and swapping is possible by simply separating vacuum state from the even state. The present paper also deals with study of effect of decoherence and noise on these states and the effect of noise on fidelity and minimum assured fidelity. It is also discussed that these schemes can also be applied to the process of entanglement diversion and entanglement swapping.
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.