Characterising two-sided quantum correlations beyond entanglement via metric-adjusted f-correlations

TL;DR

This paper introduces a new family of quantum correlation measures called quantum f-correlations, which extend beyond entanglement and are related to metric-adjusted skew informations, with applications to two-qubit systems and channels.

Contribution

It defines quantum f-correlations as a novel family of quantifiers linked to metric-adjusted skew informations, applicable to various quantum states and systems.

Findings

Quantum f-correlations vanish on classical-quantum states.

They are entanglement monotones for pure qubit-qudit states.

Closed-form expressions are derived for two-qubit systems.

Abstract

We introduce an infinite family of quantifiers of quantum correlations beyond entanglement which vanish on both classical-quantum and quantum-classical states and are in one-to-one correspondence with the metric-adjusted skew informations. The `quantum $f-$correlations' are defined as the maximum metric-adjusted $f-$correlations between pairs of local observables with the same fixed equispaced spectrum. We show that these quantifiers are entanglement monotones when restricted to pure states of qubit-qudit systems. We also evaluate the quantum $f-$correlations in closed form for two-qubit systems and discuss their behaviour under local commutativity preserving channels. We finally provide a physical interpretation for the quantifier corresponding to the average of the Wigner-Yanase-Dyson skew informations.