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Geometric quantum discord through the Schatten 1-norm

Geometric quantum discord through the Schatten 1-norm It has recently been pointed out that the geometric quantum discord, as defined by the Hilbert-Schmidt norm (2-norm), is not a good measure of quantum correlations, since it may increase under local reversible operations on the unmeasured subsystem. Here, we revisit the geometric discord by considering general Schatten p -norms, explicitly showing that the 1-norm is the only p -norm able to define a consistent quantum correlation measure. In addition, by restricting the optimization to the tetrahedron of two-qubit Bell-diagonal states, we provide an analytical expression for the 1-norm geometric discord, which turns out to be equivalent to the negativity of quantumness. We illustrate the measure by analyzing its monotonicity properties. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review A American Physical Society (APS)

Geometric quantum discord through the Schatten 1-norm

Physical Review A , Volume 87 (6) – Jun 7, 2013
4 pages

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References (3)

Publisher
American Physical Society (APS)
Copyright
©2013 American Physical Society
ISSN
1050-2947
DOI
10.1103/PhysRevA.87.064101
Publisher site
See Article on Publisher Site

Abstract

It has recently been pointed out that the geometric quantum discord, as defined by the Hilbert-Schmidt norm (2-norm), is not a good measure of quantum correlations, since it may increase under local reversible operations on the unmeasured subsystem. Here, we revisit the geometric discord by considering general Schatten p -norms, explicitly showing that the 1-norm is the only p -norm able to define a consistent quantum correlation measure. In addition, by restricting the optimization to the tetrahedron of two-qubit Bell-diagonal states, we provide an analytical expression for the 1-norm geometric discord, which turns out to be equivalent to the negativity of quantumness. We illustrate the measure by analyzing its monotonicity properties.

Journal

Physical Review AAmerican Physical Society (APS)

Published: Jun 7, 2013

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