arXiv:1012.1676 · Annals of Physics

Deterministic LOCC transformation of three-qubit pure states and entanglement transfer

Hiroyasu Tajima

Published Nov 23, 2012• 14 citations

Abstract

A necessary and sufficient condition of the possibility of a deterministic local operations and classical communication (LOCC) transformation of three-qubit pure states is given. The condition shows that the three-qubit pure states are a partially ordered set parametrized by five well-known entanglement parameters and a novel parameter; the five are the concurrences CAB, CAC, CBC, the tangle τABC and the fifth parameter J5 of Acín et al. (2000) Ref. [19], while the other new one is the entanglement charge Qe. The order of the partially ordered set is defined by the possibility of a deterministic LOCC transformation from a state to another state. In this sense, the present condition is an extension of Nielsen’s work (Nielsen (1999) [14]) to three-qubit pure states. We also clarify the rules of transfer and dissipation of the entanglement which is caused by deterministic LOCC transformations. Moreover, the minimum number of times of measurements to reproduce an arbitrary deterministic LOCC transformation between three-qubit pure states is given.

DOI: 10.1016/j.aop.2012.11.001

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