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 mean 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 generalised grand canonical ensemble, enabling entanglement certification even in complex systems with macroscopic particle numbers.
Highlights
While the occurrence and possible uses of entanglement were first studied for bipartite states, entanglement in systems containing a large number of particles is of interest both from a theoretical and from a practical point of view
If the Gibbs state entropy is larger than (2), we know that the Gibbs state is entangled
Maps can be obtained from any entanglement witness and vice versa
Summary
While the occurrence and possible uses of entanglement were first studied for bipartite states, entanglement in systems containing a large number of particles is of interest both from a theoretical and from a practical point of view. It can be shown that we can detect the same states by computing max S(ρ) ρ∈sep, Tr Hρ≤E Any state with larger entropy has to be entangled. Note that (2) is just the optimisation yielding the Gibbs state with the additional constraint of separability.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
