Mixed state localizable entanglement for continuous variables

TL;DR

This paper studies how to concentrate entanglement between two modes in multipartite Gaussian states using local Gaussian measurements, providing methods for optimal measurement strategies and discussing non-Gaussian detection.

Contribution

It proves that symmetric Gaussian states can have their entanglement maximized via homodyne detection and introduces a polynomial-root method for optimizing measurements in three-mode states.

Findings

Homodyne detection maximizes entanglement in symmetric Gaussian states.

Optimal measurement on one mode can be found by solving a high-order polynomial.

Single-photon detection is also discussed as a measurement strategy.

Abstract

We investigate localization of entanglement of multipartite mixed Gaussian states into a pair of modes by local Gaussian measurements on the remaining modes and classical communication. We provide a detailed proof that for arbitrary symmetric Gaussian state maximum entanglement can be localized by homodyne detection of either amplitude or phase quadrature on each mode. We then consider arbitrary mixed three-mode Gaussian states and show that the optimal Gaussian measurement on one mode yielding maximum entanglement among the other two modes can be determined by calculating roots of a high-order polynomial. Finally, we discuss localization of entanglement with single-photon detection.