Abstract
Quantum steering is an important quantum resource, which is intermediate between entanglement and Bell nonlocality. In this paper, we study steering witnesses for Gaussian states in continuous-variable systems. We give a definition of steering witnesses by covariance matrices of Gaussian states, and then obtain a steering criterion by steering witnesses to detect steerability of any -mode Gaussian states. In addition, the conditions for two steering witnesses to be comparable and the optimality of steering witnesses are also discussed.
Highlights
Recent works revealed that there exist Gaussian states which are only steerable by suitable non-Gaussian Positive OperatorValued Measurement (GPOVM)
We investigated steering witnesses of Gaussian states in continuous-variable systems
We give a definition of steering witnesses by covariance matrices of quantum states, and present a steering witness criterion of any (m + n)-mode Gaussian state to be unsteerable by the Hahn-Banach theorem
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. The detection of entanglement has attracted much attention in recent years (see [4,5,6,7,8,9,10,11,12,13,14,15]) Among these criteria, the entanglement witness (EW) criterion provides a sufficient and necessary condition for the separability of a bipartite quantum state ([5]). For continuous-variable systems, the authors in [25] performed a systematic investigation of EPR steering for bipartite Gaussian states by pseudospin measurements. Inspired by EW, in this paper, we will try to consider quantum EPR steering witness for Gaussian states in continuous-variable systems. A steering criterion for bipartite (m + n)-mode Gaussian states are obtained.
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