Certification of non-Gaussian Einstein-Podolsky-Rosen Steering

TL;DR

This paper introduces a new criterion for detecting non-Gaussian EPR steering using high-order observables, systematically investigates the hierarchy of such criteria, and demonstrates their application to experimentally relevant states, advancing quantum information science.

Contribution

It presents an efficient non-Gaussian steering criterion based on high-order observables and explores its application to relevant quantum states, including a scheme for creating multi-component cat states.

Findings

Established a hierarchy of non-Gaussian steering criteria.

Applied the criterion to experimentally relevant states under realistic conditions.

Proposed a feasible scheme for generating multi-component cat states.

Abstract

Non-Gaussian quantum states are a known necessary resource for reaching a quantum advantage and for violating Bell inequalities in continuous variable systems. As one kind of manifestation of quantum correlations, Einstein-Podolsky-Rosen (EPR) steering enables verification of shared entanglement even when one of the subsystems is not characterized. However, how to detect and classify such an effect for non-Gaussian states is far from being well understood. Here, we present an efficient non-Gaussian steering criterion based on the high-order observables and conduct a systematic investigation into the hierarchy of non-Gaussian steering criteria. Moreover, we apply our criterion to three experimentally-relevant non-Gaussian states under realistic conditions and, in particular, propose a feasible scheme to create multi-component cat states with tunable size by performing a suitable high-order quadrature measurement on the steering party. Our work reveals the fundamental characteristics of non-Gaussianity and quantum correlations, and offers new insights to explore their applications in quantum information processing.