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Journal of Xuzhou Institute of Technology

Research on Negativity of Bipartite Quantum System in High-dimensions

Kai Chen

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

Two kinds of definitions of Negativity are compared in theory.The obvious expression of negativity for the two-parameter class of bipartite quantum states in high-dimensions is obtained.

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Among all entanglement measures negativity arguably is the best known and most popular tool to quantify bipartite quantum correlations. It is easily computed for arbitrary states of a composite system and can therefore be applied to discuss entanglement in an ample variety of situations. However, as opposed to logarithmic negativity, its direct physical meaning has not been pointed out yet. We show that the negativity can be viewed as an estimator of how many degrees of freedom of two subsystems are entangled. As it is possible to give lower bounds for the negativity even in a device-independent setting, it is the appropriate quantity to certify quantumness of both parties in a bipartite system and to determine the minimum number of dimensions that contribute to the quantum correlations.
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.