Stabilizable Gaussian states

TL;DR

This paper investigates conditions under which Gaussian states in continuous-variable quantum systems can be stabilized despite environmental damping, providing criteria based on covariance matrices and exploring practical examples.

Contribution

It establishes necessary and sufficient conditions for stabilizing Gaussian states, extending applicability to non-Gaussian states for entanglement preservation.

Findings

Derived stabilizability conditions in terms of covariance matrices

Analyzed single and two-mode damped systems as benchmarks

Conditions applicable to non-Gaussian states for entanglement detection

Abstract

The unavoidable interaction of quantum systems with their environment usually results in the loss of desired quantum resources. Suitably chosen system Hamiltonians, however, can, to some extent, counteract such detrimental decay, giving rise to the set of stabilizable states. Here, we discuss the possibility to stabilize Gaussian states in continuous-variable systems. We identify necessary and sufficient conditions for such stabilizability and elaborate these on two benchmark examples, a single, damped mode and two locally damped modes. The obtained stabilizability conditions, which are formulated in terms of the states' covariance matrices, are, more generally, also applicable to non-Gaussian states, where they may similarly help to, e.g., discuss entanglement preservation and/or detection up to the second moments.