Comparing quantumness criteria

TL;DR

This paper compares different criteria for quantifying the quantumness of Gaussian states, revealing their equivalence in pure states and divergence under decoherence, linked to the state's phase space geometry.

Contribution

It provides a comparative analysis of quantum discord, Bell inequality violation, and non-separability criteria for Gaussian states, highlighting their geometric control.

Findings

Criteria are equivalent for pure states

Criteria diverge under decoherence

Controlled by the ellipse's semi-minor axis in phase space

Abstract

Measuring the quantumness of a system can be done with a variety of methods. In this article we compare different criteria, namely quantum discord, Bell inequality violation and non-separability, for systems placed in a Gaussian state. When the state is pure, these criteria are equivalent, while we find that they do not necessarily coincide when decoherence takes place. Finally, we prove that these criteria are essentially controlled by the semi-minor axis of the ellipse representing the state's Wigner function in phase space.