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

W Roga, D Spehner, F Illuminati

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.
LanguageEnglish
Article number235301
Number of pages52
JournalJournal of Physics A: Mathematical and Theoretical
Volume49
Issue number23
Early online date5 May 2016
DOIs
Publication statusPublished - 10 Jun 2016

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Quantification
Quantum State
Hellinger Distance
axioms
Qubit
Axioms
Subsystem
purity
Trace
Necessary Conditions

Keywords

  • quantum discord
  • geometric measures of quantum correlations
  • distances on the set of quantum states

Cite this

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Geometric measures of quantum correlations : characterization, quantification, and comparison by distances and operations. / Roga, W; Spehner, D; Illuminati, F.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 49, No. 23, 235301, 10.06.2016.

Research output: Contribution to journalArticle

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