Quantifying nonclassicality: global impact of local unitary evolutions

TL;DR

This paper establishes a quantitative link between quantum correlations and the global state change caused by local unitaries, providing an operational interpretation of quantum discord and identifying maximally quantum correlated states.

Contribution

It derives an exact relation between local unitary-induced global state change and quantum correlations, linking it to the geometric measure of discord and identifying maximally quantum correlated states.

Findings

Global state change is linked to quantum correlations.

Geometric discord measures the impact of local unitaries.

Werner states are maximally quantum correlated.

Abstract

We show that only those composite quantum systems possessing nonvanishing quantum correlations have the property that any nontrivial local unitary evolution changes their global state. We derive the exact relation between the global state change induced by local unitary evolutions and the amount of quantum correlations. We prove that the minimal change coincides with the geometric measure of discord (defined via the Hilbert- Schmidt norm), thus providing the latter with an operational interpretation in terms of the capability of a local unitary dynamics to modify a global state. We establish that two-qubit Werner states are maximally quantum correlated, and are thus the ones that maximize this type of global quantum effect. Finally, we show that similar results hold when replacing the Hilbert-Schmidt norm with the trace norm.