Problem with geometric discord

  title={Problem with geometric discord},
  author={Marco Piani},
  journal={Physical Review A},
  • M. Piani
  • Published 1 June 2012
  • Physics
  • Physical Review A
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. 
A Generalized Geometric Measurement of Quantum Discord: Exact Treatment
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 localExpand
Measurement-induced qudit geometric discord
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
Geometric measure of quantum discord with weak measurements
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
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 isExpand
Geometric quantum discord with Bures distance
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, toExpand
The geometric approach to quantum correlations: computability versus reliability
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 fromExpand
Preservation of the geometric quantum discord in noisy environments
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 beExpand
Characterizing nonclassical correlation using affinity
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
Geometric Global Quantum Discord of Two-qubit X States
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 analyticalExpand
One-norm geometric quantum discord under decoherence
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 behaviorExpand


and W
  • Liu, Arxiv preprint arXiv:1 203.6149
  • 2012
  • Brukner, et al., Arxiv preprint arXiv:1203.1629
  • 2012
  • Rev. A 85, 040301
  • 2012
  • Rev. Lett. 108, 150403
  • 2012
Physical Review A 85
  • 032325
  • 2012
and G
  • Ades so, Arxiv preprint arXiv:1205.0251
  • 2012
  • Ho rodecki, and A. Winter, Phys. Rev. Lett. 106, 220403
  • 2011
  • Rev. Let t. 106, 160401
  • 2011
  • Rev. Lett. 105, 190502
  • 2010
and K
  • Horodec ki, Rev. Mod. Phys.81, 865
  • 2009