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International Journal of Modern Physics B

ALMOST PERFECT TELEPORTATION USING 4-PARTITE ENTANGLED STATES

Hari Prakash, Naresh Chandra, R. PRAKASH, SHIVANI

Published Jul 10, 2010• 14 citations
Publisher

Abstract

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.

DOI
10.1142/s0217979210053367

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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.
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 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 ${10}^{\ensuremath{-}4}$.
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.
This paper proposes a feasible scheme for the quantum teleportation of tripartite entangled coherent states by using linear optical devices such as beam splitters, phase shifters and photo detectors. The scheme is based on the bipartite maximally entangled coherent state and the tripartite entangled coherent state with bipartite maximal entanglement as quantum channels. It shows that when the mean number of photons is equal to 2, the total minimum of the average fidelity for an arbitrary tripartite entangled state is 1 – 0.67 × 10 −3 .