Nonclassical correlations in continuous-variable non-Gaussian Werner states

TL;DR

This paper investigates nonclassical correlations beyond entanglement in continuous-variable non-Gaussian Werner states, providing analytical results and bounds for quantum discord and highlighting the importance of non-Gaussian measurements.

Contribution

It offers the first analytical evaluation of quantum discord in non-Gaussian Werner states and demonstrates the necessity of non-Gaussian measurements for optimal quantumness assessment.

Findings

Gaussian measurements are suboptimal for these states.

The gap between Gaussian and non-Gaussian discord relates to non-Gaussianity.

Nonclassical correlations remain finite even at infinite squeezing.

Abstract

We study nonclassical correlations beyond entanglement in a family of two-mode non-Gaussian states which represent the continuous-variable counterpart of two-qubit Werner states. We evaluate quantum discord and other quantumness measures obtaining exact analytical results in special instances, and upper and lower bounds in the general case. Non-Gaussian measurements such as photon counting are in general necessary to solve the optimization in the definition of quantum discord, whereas Gaussian measurements are strictly suboptimal for the considered states. The gap between Gaussian and optimal non-Gaussian conditional entropy is found to be proportional to a measure of non-Gaussianity in the regime of low squeezing, for a subclass of continuous-variable Werner states. We further study an example of a non-Gaussian state which is positive under partial transposition, and whose nonclassical correlations stay finite and small even for infinite squeezing. Our results pave the way to a systematic exploration of the interplay between nonclassicality and non-Gaussianity in continuous-variable systems, in order to gain a deeper understanding of -and to draw a bigger advantage from- these two important resources for quantum technology.