Geometric measures of quantum correlations : characterization, quantification, and comparison by distances and operations

Roga, W and Spehner, D and Illuminati, F (2016) Geometric measures of quantum correlations : characterization, quantification, and comparison by distances and operations. Journal of Physics A: Mathematical and Theoretical, 49 (23). 235301. ISSN 1751-8113 (https://doi.org/10.1088/1751-8113/49/23/235301)

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Abstract

We investigate and compare three distinguished geometric measures of bipartite quantum correlations that have been recently introduced in the literature: the geometric discord, the measurement-induced geometric discord, and the discord of response, each one defined according to three contractive distances on the set of quantum states, namely the trace, Bures, and Hellinger distances. We establish a set of exact algebraic relations and inequalities between the different measures. In particular, we show that the geometric discord and the discord of response based on the Hellinger distance are easy to compute analytically for all quantum states whenever the reference subsystem is a qubit. These two measures thus provide the first instance of discords that are simultaneously fully computable, reliable (since they satisfy all the basic Axioms that must be obeyed by a proper measure of quantum correlations), and operationally viable (in terms of state distinguishability). We apply the general mathematical structure to determine the closest classical-quantum state of a given state and the maximally quantum-correlated states at fixed global state purity according to the different distances, as well as a necessary condition for a channel to be quantumness breaking.

ORCID iDs

Roga, W ORCID logoORCID: https://orcid.org/0000-0003-4434-2515, Spehner, D and Illuminati, F;
  • Item type:Article
    ID code:56511
    Dates:
    Date
    Event
    10 June 2016
    Published
    5 May 2016
    Published Online
    10 February 2016
    Accepted
    Subjects:Science > Physics
    Department:Faculty of Science > Physics
    Depositing user: Pure Administrator
    Date deposited:25 May 2016 10:39
    Last modified:11 Nov 2024 11:26
    URI:https://strathprints.strath.ac.uk/id/eprint/56511
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