Entanglement frustration in multimode Gaussian states

TL;DR

This paper investigates entanglement frustration in multimode Gaussian states, deriving bounds on the phenomenon under energy constraints, and extends previous analyses to continuous-variable systems.

Contribution

It extends the analysis of entanglement frustration to multimode Gaussian states, providing bounds under energy constraints in different regimes.

Findings

Bounds on entanglement frustration derived for low and high energy limits.

Extension of frustration analysis from discrete to continuous-variable systems.

Insights into the limitations of multipartite entanglement in Gaussian states.

Abstract

Bipartite entanglement between two parties of a composite quantum system can be quantified in terms of the purity of one party and there always exists a pure state of the total system that maximizes it (and minimizes purity). When many different bipartitions are considered, the requirement that purity be minimal for all bipartitions gives rise to the phenomenon of entanglement frustration. This feature, observed in quantum systems with both discrete and continuous variables, can be studied by means of a suitable cost function whose minimizers are the maximally multipartite-entangled states (MMES). In this paper we extend the analysis of multipartite entanglement frustration of Gaussian states in multimode bosonic systems. We derive bounds on the frustration, under the constraint of finite mean energy, in the low and high energy limit.