Preparation of bipartite bound entangled Gaussian states in quantum optics

Abstract

The positivity of the partial transpose is in general only a necessary condition for separability. There exist quantum states that are not separable, but nevertheless are positive under partial transpose. States of this type are known as bound entangled states meaning that these states are entangled but they do not allow distillation of pure entanglement by means of local operations and classical communication (LOCC). We present a parametrization of a class of $2\times 2$ bound entangled Gaussian states for bipartite continuous-variable quantum systems with two modes on each side. We propose an experimental protocol for preparing a particular bound entangled state in quantum optics. We then discuss the robustness properties of this protocol with respect to the occupation number of thermal inputs and the degrees of squeezing.

arXiv comment10 pages, 2 figures

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• On the two-dimensional time-dependent anisotropic harmonic oscillator in a magnetic field
• Numerical detection of Gaussian entanglement and its application to the identification of bound entangled Gaussian states
• Entanglement in phase-space distribution for an anisotropic harmonic oscillator in noncommutative space
• Stabilizing Preparation of Quantum Gaussian States via Continuous Measurement
• Noisy dynamics of Gaussian entanglement: a transient bound entangled phase before separability