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Chinese Physics Letters

Three-Particle Entangled States of Continuum Variables

Fan Hong‐Yi

Published Sep 19, 2001• 14 citations
Publisher

Abstract

We introduce the three-particle entangled state of continuum variables, which is a generalization of Greenberger-Horne-Zeilinger entangled states composed of discrete states. The completeness relation and partly non-orthonormal property of such states are proven. Their Schmidt decomposition is manifestly shown and their generation is briefly discussed.

DOI
10.1088/0256-307x/18/10/302

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We show that not all four-party pure states are Greenberger-Horne-Zeilinger (GHZ) reducible (i.e., can be generated reversibly from a combination of two-, three-, and four-party maximally entangled states by local quantum operations and classical communication asymptotically). We also present some properties of the relative entropy of entanglement for those three-party pure states that are GHZ reducible, and then we relate these properties to the additivity of the relative entropy of entanglement.