Quantification of Gaussian quantum steering

TL;DR

This paper introduces a new quantifiable measure of Gaussian quantum steering for continuous variable systems, linking it to quantum key distribution and confirming a conjecture about bound entangled states.

Contribution

It provides a computable measure of Gaussian steering, relates it to coherent information and entanglement, and proves a strengthened version of Peres' conjecture in the Gaussian regime.

Findings

The measure reduces to coherent information for two-mode states.

Steering measure never exceeds entanglement, equals it for pure states.

Steering bound entangled Gaussian states with Gaussian measurements is impossible.

Abstract

Einstein-Podolsky-Rosen steering incarnates a useful nonclassical correlation which sits between entanglement and Bell nonlocality. While a number of qualitative steering criteria exist, very little has been achieved for what concerns quantifying steerability. We introduce a computable measure of steering for arbitrary bipartite Gaussian states of continuous variable systems. For two-mode Gaussian states, the measure reduces to a form of coherent information, which is proven never to exceed entanglement, and to reduce to it on pure states. We provide an operational connection between our measure and the key rate in one-sided device-independent quantum key distribution. We further prove that Peres' conjecture holds in its stronger form within the fully Gaussian regime: namely, steering bound entangled Gaussian states by Gaussian measurements is impossible.