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.

Coherence, entanglement, and quantumness in closed and open systems with conserved charge, with an application to many-body localization

“…We note that this last result is also implied by Ref. [90], which establishes the difference between the QFI for the total charge and the sum of the QFI for the subsystem charges, as a witness of bipartite discord (also without charge conservation).…”

“…Interestingly, the QFI (2) itself for a nondegenerate observable with a fixed spectrum which is minimized over a local choice of basis can also be viewed as a measure of multipartite discord (see [103,104] and cf. [55,56,90]), and in this case the choice of computational basis again provides a faithful upper bound on MPD.…”

A Unified Approach to Local Quantum Uncertainty and Interferometric Power by Metric Adjusted Skew Information

“…The partial order relation is stronger that the usual order relation ≤, and it renders (F op , ) into a lattice with f min (t) = 2t t + 1 and f max (t) = t + 1 2 (8) as, respectively, the minimal element and maximal element. Furthermore, f g if and only if h f ≥ h g almost everywhere,…”

“…This discovery triggered theoretical and experimental studies to understand the physical meaning of quantum discord, and the potential use of it as a resource for quantum technologies [4]. Relying on the known interplay between the geometrical and physical properties of mixed states [5,6], a stream of works employed information geometry techniques to construct quantifiers of quantum discord [7][8][9][10][11][12]. In particular, two of the most popular ones are the Local Quantum Uncertainty (LQU) and the Interferometric Power (IP) [13,14].…”

A unified approach to Local Quantum Uncertainty and Interferometric Power by Metric Adjusted Skew Information

“…The discovery triggered theoretical and experimental studies to understand the physical meaning of quantum discord, and the potential use of it as a resource for quantum technologies [7]. Relying on the known interplay between geometrical and physical properties of mixed states [8,9], a stream of works employed information geometry techniques to construct quantifiers of quantum discord [10][11][12][13][14][15]. In particular, two of the most popular ones are the Local Quantum Uncertainty (LQU) and the Interferometric Power (IP) [1,2].…”