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Journal of Xuzhou Institute of Technology

Negativity of a Two-parameter Class of θ-States in mn Quantum System

Liu Dong-dong

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

A two-parameter class of θ-states in quantum system are discovered. And the analytic expression of negativity of these states which are not D-computable states is obtained.

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Entanglement for a three-parameter class of states in bipartite quantum system is investigated.The concurrence for these states in 2n quantum system is calculated and their lower bound of the entanglement of formation is discussed.The negativity for these states in mn(2≤m≤n) quantum system is calculated and the analytic expressions are obtained.Investigation reveals that for θ=π/4,entanglement of the states reaches its maximum,and the states come down to the two-parameter class of states researched by some authors.For these three-parameter states in 2n quantum system,all PPT states are separable,and all NPT states are entangled.But for higher dimensional three-parameter states,the similar conclusion does not exist.
We exhibit a two-parameter class of states ρ (α,γ) in a 2 ⊗ n quantum system for n ⩾ 3, which can be obtained from an arbitrary state by means of local quantum operations and classical communication, and which are invariant under all bilateral operations on a 2 ⊗ n quantum system. We calculate the negativity of ρ (α,γ) , and a lower bound and a tight upper bound on its entanglement of formation. It follows from this calculation that the entanglement of formation of ρ (α,γ) cannot exceed its negativity.
Any arbitrary state in bipartite quantum system can be transformed into a two-parameter class of states by means of local quantum operation and classical communication.In this paper,the quantum relative entropy of entanglement for this kind of states is calculated,the nearest separable states are found and the analytic expression of the entanglement is obtained.The comparation with two other measures of entanglement,the negativity and the entanglement of formation,is also made.The sequence of three measures from high to low is the negativity,the entanglement of formation and the relative entropy of entanglement.