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Journal of Liaoning Normal University

Recent Progress on Entanglement of Multipartite Pure States

Guoying Lu

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

Recent research progress on quantifying and classifying entanglement for a given multipartite pure state is summarized.A new measure for the entanglement is defined,which can be used to distinguish entanglement properties pure states from one another,and quantify the measure of the entanglement for multipartite pure states.

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In this paper, we consider the problem of how to quantify entanglement for any multipartite quantum states. For bipartite pure states partial entropy is a good entanglement measure. By using partial entropy, we firstly introduce the Combinatorial Entropy of Fully entangled states (CEF) which can be used to quantify entanglement for any fully entangled pure states. In order to quantify entanglement for any multipartite states we also need another concept the Entanglement Combination (EC) which can be used to completely describe the entanglement between any parties of the given quantum states. Combining CEF with EC, we define the Combinatorial Entropy (CE) for any multipartite pure states and present some nice properties which indicate CE is a good entanglement measure. Finally, we point out the feasibility of extending these three concepts to mixed quantum states.
A natural way of quantifying the degree of entanglement for a pure quantum state is to compare how far this state is from the set of all unentangled pure states. This geometric measure of entanglement is explored for bipartite and multipartite pure and mixed states. It is determined analytically for arbitrary two‐qubit mixed states and for generalized Werner and isotropic states. It is also applied to certain multipartite mixed states, including two multipartite bound entangled states discovered by Smolin and Dür. Moreover, the geometric measure of entanglement is applied to the ground state of the Ising model in a transverse magnetic field. From this model the entanglement is shown to exhibit singular behavior at the quantum critical point.