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OSA Workshop on Entanglement and Quantum Decoherence

Multi-party quantum correlation and entanglement

Li You

Published Jan 1, 2008• 0 citations
Publisher

Abstract

A characterization of the complete correlation structure in an n-party system is proposed in terms of a series of (k, n) threshold classical secret sharing protocols (2 ≤ k ≤ n). The total correlation is shown to be the sum of independent correlations of 2-, 3-,…, n-parties. Our result unifies several earlier scattered works, and shines new light at the important topic of multi-party quantum entanglement. As an application, we explicitly construct the hierarchy of correlations in an n-qubit graph state.

DOI
10.1364/weqd.2008.eas2

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A characterization of the complete correlation structure in an n-party system is proposed in terms of a series of (k, n) threshold classical secret sharing protocols (2 ≤ k ≤ n). The total correlation is shown to be the sum of independent correlations of 2-, 3-,…, n-parties. Our result unifies several earlier scattered works, and shines new light at the important topic of multi-party quantum entanglement. As an application, we explicitly construct the hierarchy of correlations in an n-qubit graph state.
A characterization of the complete correlation structure in an nnn-party system is proposed in terms of a series of (k,n)(k,n)(k,n) threshold classical secret sharing protocols (2≤k≤n2\le k\le n2≤k≤n). The total correlation is shown to be the sum of independent correlations of 2-, 3-,........., nnn-parties. Our result unifies several earlier scattered works, and shines new light at the important topic of multi-party quantum entanglement. As an application, we explicitly construct the hierarchy of correlations in an nnn-qubit graph state.
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Strong polygamy of multi-party qqq-expected quantum correlations
We show that the polygamous nature of multi-party quantum correlations can be characterized in a {\em stronger} form based on Tsallis qqq-entropy and qqq-expectation value. By considering the amount of entanglement that can be distributed in multi-party systems, we establish a class of strong polygamy inequalities of multi-party entanglement in terms of Tsallis qqq-entropy and qqq-expectation for q≥1q \geq 1q≥1. Our new class of inequalities is in fact tighter than the usual polygamy inequalities of multi-party entanglement, and the tightness is explicitly illustrated by an example. Moreover, our new class of inequalities is concerned with the qqq-expected entanglement distributed between a single party and any possible subsets of the rest parties whereas the usual polygamy inequality only considers the entanglement between a single party and another. We further establish the equivalence between strong polygamy inequalities of quantum entanglement and quantum discord distributed in multi-party quantum systems.