Bipartite bound entanglement in continuous variables through deGaussification

TL;DR

This paper proposes a feasible method to generate and detect bipartite bound entangled states in continuous variables using optical systems, involving non-Gaussian operations and advanced mathematical criteria.

Contribution

It introduces a new class of PPT bound entangled states in continuous variables and a practical scheme for their experimental realization and verification.

Findings

States are positive under partial transposition (PPT) and entangled.

Preparation method is unconditional after calibration.

Bound entanglement is verified using advanced mathematical criteria.

Abstract

We introduce a class of bipartite entangled continuous variable states that are positive under partial transposition operation, i.e., PPT bound entangled. These states are based on realistic preparation procedures in optical systems, being thus a feasible option to generate and observe genuinely bipartite bound entanglement in high precision experiments. One fundamental step in our scheme is to perform a non-Gaussian operation over a single-mode Gaussian state; this deGaussification procedure is achieved through a modified single-photon addition, which is a procedure that has currently being investigated in diverse optical setups. Although dependent on a single-photon detection in a idler channel, the preparation can be made unconditional after a calibration of the apparatus. The detection and proof of bound entanglement is made by means of the Range Criterion, theory of Hankel operators and Gerschgorin Disk s perturbation theorems.