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Communications in Theoretical Physics

Study of Concurrence and D-Concurrence on Two-Qubits Resulted in Pair Coherent States in Language of SU(2) Coherent States

S. Salimi, A. Mohammadzade

Published Aug 1, 2011• 3 citations
Publisher

Abstract

Pair coherent state, is a state of a two-mode radiation field that is known as a state with non-gaussian wave function. In this paper, study on the pair coherent state, we notice that with superposition of two first terms of this states, one two-qubits formed. Because of the importance of two-qubits in theory of quantum entanglement, with two different measures with the title of concurrence and D-concurrence, we have studied the amount of entanglement and discussed its details. At the end, we describe these measures for pair coherent states as a function of the amplitude of the SU(2) coherent states.

DOI
10.1088/0253-6102/56/2/08

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Pair coherent state, is a state of a two-mode radiation field that is known as a state with non-gaussian wave function. In this paper, study on the pair coherent state, we notice that with superposition of two first terms of this states, one two-qubits formed. Because of the importance of two-qubits in theory of quantum entanglement, with two different measures with the title of concurrence and D-concurrence, we have studied the amount of entanglement and discussed its details. At the end, we describe these measures for pair coherent states as a function of the amplitude of the SU(2) coherent states.
Entanglement transfer from the superposition states of the pair coherent states or the SU(1,1) coherent states to two initially separable qubits is investigated. The entropy of the superposition states has a novel property: there exists a maximum value when the phase difference between the two 2-mode coherent states is π. In the process of entanglement transfer from these superposition states to qubits, it is found that the qubits have the largest possible entanglement at the maximum of the entropy of the initial field, which shows a relationship between the entanglement of the initial field and that of the qubits. The concurrence of the qubits can periodically approach unity when the parameters of the initial field are properly chosen and the two qubits are initially at the ground states.
Abstract We investigate the entanglement of a bipartite partly non-orthogonal state of the form | ϕ ⟩ = u | ξ ⟩ 1 ⊗ | 1 ⟩ 2 + v | ξ ⟩ 1 ⊗ | 0 ⟩ 2 + w | ξ ′ ⟩ 1 ⊗ | 1 ⟩ 2 + z | ξ ′ ⟩ 1 ⊗ | 0 ⟩ 2 through 1 2 -spin coherent states by adopting the concurrence as a measure to quantify the degree of entanglement of the two-qubit system. After, we study the amount of entanglement of mixed states represented by a statistical mixture of partly non-orthogonal bipartite pure states. We also express the lower and upper bounds of the squared concurrence of mixed states in terms of the amplitudes of spin coherent states.
In this paper, after a brief review on the entangled coherent state, a general form of the entangled nonlinear coherent state has been introduced based on the nonlinear coherent states approach. By choosing particular f-deformation functions, theoretical schemes for generation of two distinct classes of such states associated with SU(1,1) and SU(2) groups are presented. The entanglement characteristic of the corresponding entangled coherent states has been studied by evaluating the concurrence. In the continuation, other nonclassical behaviors of the produced states have been analyzed by investigating sub-Poissonian photon statistics, the oscillatory photon number distribution, one- and two-mode quadrature squeezing, and sum and difference squeezing. Accordingly, in addition to their entanglement property, other nonclassicality features of the introduced states are well established in detail.