Quantify Entanglement for Multipartite Quantum States

TL;DR

This paper introduces a new framework for quantifying entanglement in multipartite quantum states using combinatorial entropy, applicable to both pure and mixed states, advancing the measurement of quantum correlations.

Contribution

It proposes the Combinatorial Entropy (CE) as a novel entanglement measure for multipartite states, combining CEF and EC concepts, with potential extension to mixed states.

Findings

CEF effectively quantifies entanglement in fully entangled pure states.

CE possesses desirable properties as an entanglement measure.

The framework suggests feasibility for extension to mixed states.

Abstract

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.