Degrees of entanglement for multipartite systems

TL;DR

This paper introduces a unified mathematical framework using tensor isomorphism to quantify entanglement in pure multipartite quantum states, providing insights into separability and robustness under measurements.

Contribution

It presents a novel tensor-based scheme for characterizing multipartite entanglement, including conditions for separability and measures for entanglement degrees.

Findings

Provides a set of determinants for quantifying entanglement.

Offers necessary and sufficient conditions for separability.

Includes a method for rough entanglement estimation in large systems.

Abstract

We propose a unified mathematical scheme, based on a classical tensor isomorphism, for characterizing entanglement that works for pure states of multipartite systems of any number of particles. The degree of entanglement is indicated by a set of absolute values of the determinants for each subspace of the multipartite systems. Unlike other schemes, our scheme provides indication of the degrees of entanglement when the qubits are measured or lost successively, and leads naturally to the necessary and sufficient conditions for multipartite pure states to be separable. For systems with a large number of particles, a rougher indication of the degree of entanglement is provided by the set of mean values of the determinantal values for each subspace of the multipartite systems.