Investigating Einstein-Podolsky-Rosen steering of continuous variable bipartite states by non-Gaussian pseudospin measurements

TL;DR

This paper systematically investigates EPR steering in continuous variable bipartite states using non-Gaussian pseudospin measurements, revealing regimes where such measurements outperform Gaussian ones in detecting steerability, especially under noise.

Contribution

It extends previous work by deriving density matrix elements for two-mode squeezed thermal states and analyzing the effectiveness of non-Gaussian pseudospin measurements for steering detection.

Findings

Non-Gaussian measurements can better detect steering in noisy Gaussian states.

Gaussian pseudospin observables are less sensitive than Gaussian measurements for steering.

Pseudospin measurements are more effective for non-Gaussian Werner states.

Abstract

EPR steering is an asymmetric form of correlations which is intermediate between quantum entanglement and Bell nonlocality, and can be exploited for quantum communication with one untrusted party. In particular, steering of continuous variable Gaussian states has been extensively studied as a manifestation of the EPR paradox. While most of these studies focused on quadrature measurements for steering detection, two recent works revealed that there exist Gaussian states which are only steerable by non-Gaussian measurements. In this paper we perform a systematic investigation of EPR steering of bipartite Gaussian states by pseudospin measurements, complementing and extending previous findings. We first derive the density matrix elements of two-mode squeezed thermal states in the Fock basis, which may be of independent interest. We then use such a representation to investigate steering of these states as detected by a nonlinear criterion, based on second moments of the pseudospin correlation matrix. This analysis reveals previously unexplored regimes where non-Gaussian measurements are more effective than Gaussian ones to witness steering of Gaussian states in the presence of local noise. We further consider an alternative set of pseudospin observables, whose expectation value can be expressed compactly in terms of Wigner functions for all two-mode Gaussian states. However, according to the adopted criterion, these observables are found to be always less sensitive than Gaussian observables for steering detection. Finally, we investigate continuous variable Werner states, which are non-Gaussian mixtures of Gaussian states, and find that pseudospin measurements are always more effective than Gaussian ones to reveal their steerability. Our results provide useful insights on the role of non-Gaussian measurements in characterizing quantum correlations of Gaussian and non-Gaussian states.