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Chinese Physics Letters

Entangled States Based on Two Coherent States 3π/2 out of Phase

Muhammad Ashfaq Ahmad, Shutian Liu

Published Oct 26, 2006• 10 citations
Publisher

Abstract

Entangled states based on two coherent states 3π/2 out of phase with each other, i.e. |α⟩ and e i ϕ |− i α⟩, as well as on a special state with a relative phase ϕ = |α| 2 , are constructed. By analysing the amount of entanglement it is evident that entangled states based on this special state can be used as an excellent resource for quantum teleportation. It is also revealed that these entangled states possess some nonclassical features.

DOI
10.1088/0256-307x/23/11/022

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Entangled states based on two coherent states 3π/2 out of phase with each other, i.e. |α⟩ and e i ϕ |− i α⟩, as well as on a special state with a relative phase ϕ = |α| 2 , are constructed. By analysing the amount of entanglement it is evident that entangled states based on this special state can be used as an excellent resource for quantum teleportation. It is also revealed that these entangled states possess some nonclassical features.
Nonclassical features of entangled coherent states (two-mode superposition coherent states) based on two coherent states shifted in phase by π/2 are discussed. Analysis of Cauchy–Schwartz inequality, two-mode quadrature squeezing, oscillatory and sub-Poissonian photon statistics show that nonclassicality exists for these states. Furthermore, it is also observed that special states have remarkably strong nonclassical properties than the entangled coherent states based on famous even–odd coherent states.
When a superposition $(|\ensuremath{\alpha}〉\ensuremath{-}|\ensuremath{-}\ensuremath{\alpha}〉)$ of two coherent states with opposite phase falls upon a 50-50 beam splitter, the resulting state is entangled. Remarkably, the amount of entanglement is exactly 1 ebit, irrespective of \ensuremath{\alpha}, as was recently discovered by Hirota and Sasaki [LANL e-print quant-ph/0101018]. Here we discuss decoherence properties of such states and give a simple protocol that teleports one qubit encoded in Schr\"odinger cat states.
We consider the quantum superposition of two coherent states shifted in phase by 3π/2, |α⟩ and |− i α⟩, as well as special states that are characterized solely with respect to amplitude α. According to analysis of nonclassical properties such as oscillatory and sub-Poissonian distribution of photon numbers, photon antibunching, quadrature squeezing, and negativity of Wigner function, it is concluded that the considered superposition state is a nonclassical state. Also, the special state is found to exhibit even stronger nonclassical features when relative phase ϕ of the superposition is equal to the average photon number |α| 2 .
We propose a scheme to teleport a two-mode entangled coherent state encoded with two-qubit information, which is better than the two schemes recently proposed by Liao and Kuang ( 2007 J. Phys. B: At. Mol. Opt. Phys. 40 1183 ) and by Phien and Nguyen (2008 Phys. Lett. A 372 2825) in that our scheme gives higher value of minimum assured fidelity and minimum average fidelity without using any nonlinear interactions. For involved coherent states | ± α⟩, minimum average fidelity in our case is ⩾0.99 for |α| ⩾ 1.6 (i.e. |α| 2 ⩾ 2.6), while previously proposed schemes referred above report the same for |α| ⩾ 5 (i.e. |α| 2 ⩾ 25). Since it is very challenging to produce superposed coherent states of high coherent amplitude (|α|), our teleportation scheme is at the reach of modern technology.