# Problem with geometric discord

@article{Piani2012ProblemWG, title={Problem with geometric discord}, author={Marco Piani}, journal={Physical Review A}, year={2012}, volume={86}, pages={034101} }

We argue that the geometric discord introduced in [B. Dakic, V. Vedral, and C. Brukner, Phys. Rev. Lett. 105, 190502 (2010)] is not a good measure for the quantumness of correlations, as it can increase even under trivial local reversible operations of the party whose classicality/non-classicality is not tested. On the other hand it is known that the standard, mutual-information based discord does not suffer this problem; a simplified proof of such a fact is given.

#### 188 Citations

A Generalized Geometric Measurement of Quantum Discord: Exact Treatment

- Mathematics, Physics
- 2014

A generalization of the geometric measure of quantum discord is introduced in this article, based on Hellinger distance. Our definition has virtues of computability and independence of local… Expand

Measurement-induced qudit geometric discord

- Mathematics, Physics
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We study measurement-induced geometric discord based on the trace norm and generalize some properties known for qutrits to qudits. Previous preliminary results for bipartite qutrit systems (i.e. d =… Expand

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It is found that the quantum correlation can be extracted by a sequence of infinitesimal weak measurements and the results are demonstrated by explicit example. Expand

Toward computability of trace distance discord

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It is known that a reliable geometric quantifier of discord-like correlations can be built by employing the so-called trace distance, which is used to measure how far the state under investigation is… Expand

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- Physics
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We define a new measure of quantum correlations in bipartite quantum systems given by the Bures distance of the system state to the set of classical states with respect to one subsystem, that is, to… Expand

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We propose a modified metric based on the Hilbert?Schmidt norm and adopt it to define a rescaled version of the geometric measure of quantum discord. Such a measure is found not to suffer from… Expand

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- Physics
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Abstract Geometric description of quantum correlations is favored for their distinct physical significance. Geometric discords based on the trace distance and the Bures distance are shown to be… Expand

Characterizing nonclassical correlation using affinity

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This article proposes a new version of geometric discord using affinity that satisfies all the necessary criteria of a good measure of quantum correlation for bipartite system and resolves local ancilla problem. Expand

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In this paper, we find that the geometric global quantum discord proposed by Xu and the total quantum correlations proposed by Hassan and Joag are identical. Moreover, we work out the analytical… Expand

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Geometric quantum discord is a well-defined measure of quantum correlation if Schatten 1-norm (trace norm) is adopted as a distance measure. Here, we analytically investigate the dynamical behavior… Expand

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