A nonconvex entanglement monotone determining the characteristic length of entanglement distribution in continuous-variable quantum networks

TL;DR

This paper introduces a new continuous-variable entanglement measure, the ratio negativity, which effectively characterizes entanglement decay in quantum networks, enabling better analysis of large-scale quantum communication.

Contribution

It presents a novel nonconvex entanglement monotone for CV systems, providing a scalable way to assess entanglement distribution in quantum networks.

Findings

The ratio negativity determines the exponential decay of entanglement in Gaussian states.

The measure is simple, scalable, and applicable to large quantum networks.

It opens new avenues for applying statistical physics to quantum network analysis.

Abstract

Quantum networks (QNs) promise to enhance the performance of various quantum technologies in the near future by distributing entangled states over long distances. The first step towards this is to develop novel entanglement measures that are both informative and computationally tractable at large scales. While numerous such entanglement measures exist for discrete-variable (DV) systems, a comprehensive exploration for experimentally preferred continuous-variable (CV) systems is lacking. Here, we introduce a class of CV entanglement measures, among which we identify a nonconvex entanglement monotone -- the ratio negativity, which possesses a simple, scalable form that determines the exponential decay of optimal entanglement swapping on a chain of pure Gaussian states. This characterization opens avenues for leveraging statistical physics tools to analyze swapping-protocol-based CV QNs.