Non-zero total correlation means non-zero quantum correlation

TL;DR

This paper explores super quantum discord, an extension of quantum discord based on weak measurements, showing it detects non-zero quantum correlations in states with non-zero mutual information.

Contribution

It establishes conditions for zero super quantum discord and demonstrates that non-zero correlations are always detectable via weak measurements.

Findings

Super quantum discord is zero only for product states.

Non-zero correlations can be detected with weak measurements.

Application to assisted state-discrimination method.

Abstract

We investigated the super quantum discord based on weak measurements. The super quantum discord is an extension of the standard quantum discord defined by projective measurements and also describes the quantumness of correlations. We provide some equivalent conditions for zero super quantum discord by using quantum discord, classical correlation and mutual information. In particular, we find that the super quantum discord is zero only for product states, which have zero mutual information. This result suggests that non-zero correlations can always be detected using the quantum correlation with weak measurements. As an example, we present the assisted state-discrimination method.