A Witness of Multipartite Entanglement Strata

TL;DR

This paper introduces an entanglement witness for multipartite quantum states based on correlation functions, capable of detecting various entanglement structures including bound entanglement, even at high temperatures.

Contribution

It presents a novel entanglement witness that assesses the degree of multipartite entanglement in mixed states using correlation functions, applicable to large systems.

Findings

Witness can detect bound-entangled states.

Entanglement persists at arbitrary temperature in thermodynamic limit.

Can certify the number of separable qubits in a state.

Abstract

We describe an entanglement witness for $N$-qubit mixed states based on the properties of $N$-point correlation functions. Depending on the degree of violation, this witness can guarantee that no more than $M$ qubits are separable from the rest of the state for any $M\leq N$, or that there is some genuine $M$-party or greater multipartite entanglement present. We illustrate the use our criterion by investigating the existence of entanglement in thermal stabilizer states, where we demonstrate that the witness is capable of witnessing bound-entangled states. Intriguingly, this entanglement can be shown to persist in the thermodynamic limit at arbitrary temperature.