Detecting and estimating continuous-variable entanglement by local orthogonal observables

TL;DR

This paper introduces a new family of entanglement witnesses based on continuous-variable local orthogonal observables, enabling detection and estimation of entanglement in Gaussian and non-Gaussian states, including bound entangled states.

Contribution

It develops a novel entanglement detection method using CVLOOs that is equivalent to the realignment criterion and applicable to bound entangled states.

Findings

Detects bound entanglement in 2+2 mode Gaussian states

Provides lower bounds for entanglement measures in continuous-variable states

Equivalent to the realignment criterion for optimal CVLOOs

Abstract

Entanglement detection and estimation are fundamental in quantum information science. Compared with discrete-variable states, for which lots of efficient entanglement detection criteria and lower bounds of entanglement measures have been proposed, the continuous-variable entanglement is much less understood. Here we shall present a family of entanglement witnesses based on continuous-variable local orthogonal observables (CVLOOs) to detect and estimate entanglement of Gaussian and non-Gaussian states, especially for bound entangled states. By choosing an optimal set of CVLOOs our entanglement witness is equivalent to the realignment criterion and can be used to detect bound entanglement of a class of 2+2 mode Gaussian states. Via our entanglement witness, lower bounds of two typical entanglement measures for arbitrary two-mode continuous-variable states are obtained.