Thursday, January 17, 2013

1301.3526 (Tommaso Tufarelli et al.)

The geometric approach to quantum correlations: Computability versus

Tommaso Tufarelli, Tom MacLean, Davide Girolami, Ruggero Vasile, Gerardo Adesso
The geometric discord has enjoyed recognition as a widely employed quantifier of quantum correlations, because of its computability and experimental accessibility. However, due to the use of the Hilbert-Schmidt metric, it fails to meet reliability criteria whenever the considered states are highly mixed, the dimensionality of the system is not kept fixed or local operations are performed on the unmeasured party [Piani M 2012 Phys. Rev. A 86 034101]. So far, correcting such issues by the use of a more suitable distance has typically come at the high cost of giving up explicit computability. Taking into account these points, we argue about the employability of the Hilbert-Schmidt metric for the quantification of quantum correlations. As constructive example, we propose a distance measure which is not biased by state purity, whilst preserving computability. By considering some paradigmatic case studies, we then show that the resulting 'rescaled discord' can be a reliable indicator of the presence of bipartite quantum correlations, while the original geometric discord fails to be informative.
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