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International Journal of Modern Physics B

ENTANGLEMENT OF TWO-QUBIT NONORTHOGONAL STATES

K. Berrada, A. Chafik, Hichem Eleuch, Y. Hassouni

Published Mar 30, 2009• 12 citations
Publisher

Abstract

We studied the entangled two-qubit nonorthogonal pure states through spin coherent states. Using the concurrence as a measure of entanglement we express it as a function of the amplitudes of those states and find conditions for maximal and minimal entanglement.
DOI
10.1142/s0217979209052169

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In the present paper, we examine the quantum entanglement for more general states of two-qubit system in the context of spin coherent states (SCSs). We consider the concurrence as a quantifier of entanglement and express it in terms of SCSs. We determine new set of maximally entangled conditions that provide the maximal amount of entanglement for certain values of the amplitudes of SCSs for the case of pure states. Finally, we examine the entanglement of a class of mixed states of the two qubits and provide the range in which the entanglement value is maximal with respect to the values of the amplitudes of SCSs.
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.