Efficient $k$-separability criteria for mixed multipartite quantum states

TL;DR

This paper introduces efficient $k$-separability criteria for detecting and classifying entanglement in mixed multipartite quantum states, enabling practical experimental implementation without complex computations.

Contribution

The authors develop new $k$-separability criteria applicable to arbitrary dimensional systems, capable of identifying various entangled states without optimization or eigenvalue calculations.

Findings

Criteria can distinguish $n-1$ classes of inseparable states

Detects important states like GHZ, W, and anti W states

Requires at most $ ext{O}(n^2)$ local measurements

Abstract

We investigate classification and detection of entanglement of multipartite quantum states in a very general setting, and obtain efficient $k$-separability criteria for mixed multipartite states in arbitrary dimensional quantum systems. These criteria can be used to distinguish $n-1$ different classes of multipartite inseparable states and can detect many important multipartite entangled states such as GHZ states, W states, anti W states, and mixtures thereof. They detect $k$-nonseparable $n$-partite quantum states which have previously not been identified. Here $k=2,3,\cdots,n$. No optimization or eigenvalue evaluation is needed, and our criteria can be evaluated by simple computations involving components of the density matrix. Most importantly, they can be implemented in today's experiments by using at most $\mathcal{O}(n^2)$ local measurements.