Witnessing entanglement by proxy

TL;DR

This paper introduces a method to detect entanglement in high-temperature macroscopic systems using proxy observables, surpassing previous techniques and enabling certification without local measurements.

Contribution

It proposes a novel approach employing macroscopic observables as proxies for entanglement, outperforming existing methods and applicable to complex systems with many particles.

Findings

Proxy witnesses can certify entanglement at higher temperatures.

Linear and semi-definite relaxations improve detection capabilities.

Method applicable to systems with macroscopic particle numbers.

Abstract

Entanglement is a ubiquitous feature of low temperature systems and believed to be highly relevant for the dynamics of condensed matter properties and quantum computation even at higher temperatures. The experimental certification of this paradigmatic quantum effect in macroscopic high temperature systems is constrained by the limited access to the quantum state of the system. In this paper we show how macroscopic observables beyond the energy of the system can be exploited as proxy witnesses for entanglement detection. Using linear and semi-definite relaxations we show that all previous approaches to this problem can be outperformed by our proxies, i.e. entanglement can be certified at higher temperatures without access to any local observable. For an efficient computation of proxy witnesses one can resort to a generalized grand canonical ensemble, enabling entanglement certification even in complex systems with macroscopic particle numbers.