Nonclassical steering and the Gaussian steering triangoloids

TL;DR

This paper introduces nonclassical steering (NS) in Gaussian quantum states, providing a criterion for its detection, exploring its relation to entanglement and EPR-steering, and offering a new operational interpretation of P-nonclassicality.

Contribution

It defines and characterizes nonclassical steering in Gaussian states, deriving a necessary and sufficient condition for TMSTs, and generalizes NS to all Gaussian states with a new operational meaning.

Findings

Derived a necessary and sufficient condition for nonclassical steering in TMSTs.

Showed that entanglement is only necessary for NS, not sufficient.

Identified a new operational interpretation of P-nonclassicality as enabling one-party entanglement verification.

Abstract

Nonclassicality according to the singularity or negativity of the Glauber P-function is a powerful resource in quantum information, with relevant implications in quantum optics. In a Gaussian setting, and for a system of two modes, we explore how P-nonclassicality may be conditionally generated or influenced on one mode by Gaussian measurements on the other mode. Starting from the class of two-mode squeezed thermal states (TMST), we introduce the notion of nonclassical steering (NS) and the graphical tool of Gaussian triangoloids. In particular, we derive a necessary and sufficient condition for a TMST to be nonclassically steerable, and show that entanglement is only necessary. We also apply our criterion to noisy propagation of a twin-beam state, and evaluate the time after which NS is no longer achievable. We then generalize the notion of NS to the full set of Gaussian states of two modes, and recognize that it may occur in a weak form, which does not imply entanglement, and in a strong form that implies EPR-steerability and, a fortiori, also entanglement. These two types of NS coincide exactly for TMSTs, and they merge with the previously known notion of EPR steering. By the same token, we recognize a new operational interpretation of P-nonclassicality: it is the distinctive property that allows one-party entanglement verification on TMSTs.