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

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.