Quantum steering of Gaussian states via non-Gaussian measurements

TL;DR

This paper introduces a new formalism using non-Gaussian measurements to detect quantum steering in Gaussian states, revealing steering phenomena missed by traditional Gaussian criteria, and impacting fundamental understanding and applications.

Contribution

It develops a formalism based on local uncertainty relations of non-Gaussian measurements to detect quantum steering in Gaussian states where Gaussian criteria fail.

Findings

Non-Gaussian measurements reveal steering in Gaussian states missed by Gaussian criteria

Modification of monogamy relations and one-way steering in Gaussian states

Potential for new applications and fundamental insights beyond Gaussian regime

Abstract

Quantum steering---a strong correlation to be verified even when one party or its measuring device is fully untrusted---not only provides a profound insight into quantum physics but also offers a crucial basis for practical applications. For continuous-variable (CV) systems, Gaussian states among others have been extensively studied, however, mostly confined to Gaussian measurements. While the fulfillment of Gaussian criterion is sufficient to detect CV steering, whether it is also necessary for Gaussian states is a question of fundamental importance in many contexts. This critically questions the validity of characterizations established only under Gaussian measurements like the quantification of steering and the monogamy relations. Here, we introduce a formalism based on local uncertainty relations of non-Gaussian measurements, which is shown to manifest quantum steering of some Gaussian states that Gaussian criterion fails to detect. To this aim, we look into Gaussian states of practical relevance, i.e. two-mode squeezed states under a lossy and an amplifying Gaussian channel. Our finding significantly modifies the characteristics of Gaussian-state steering so far established such as monogamy relations and one-way steering under Gaussian measurements, thus opening a new direction for critical studies beyond Gaussian regime.