Interplay between computable measures of entanglement and other quantum correlations

Davide Girolami and Gerardo Adesso
Phys. Rev. A 84, 052110 – Published 15 November 2011

Abstract

Composite quantum systems can be in generic states characterized not only by entanglement but also by more general quantum correlations. The interplay between these two signatures of nonclassicality is still not completely understood. In this work we investigate this issue, focusing on computable and observable measures of such correlations: entanglement is quantified by the negativity N, while general quantum correlations are measured by the (normalized) geometric quantum discord DG. For two-qubit systems, we find that the geometric discord reduces to the squared negativity on pure states, while the relationship DGN2 holds for arbitrary mixed states. The latter result is rigorously extended to pure, Werner, and isotropic states of two-qudit systems for arbitrary d, and numerical evidence of its validity for arbitrary states of a qubit and a qutrit is provided as well. Our results establish an interesting hierarchy, which we conjecture to be universal, between two relevant and experimentally friendly nonclassicality indicators. This ties in with the intuition that general quantum correlations should at least contain and in general exceed entanglement on mixed states of composite quantum systems.

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  • Received 14 June 2011

DOI:https://doi.org/10.1103/PhysRevA.84.052110

©2011 American Physical Society

Authors & Affiliations

Davide Girolami* and Gerardo Adesso

  • School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom

  • *pmxdg1@nottingham.ac.uk
  • gerardo.adesso@nottingham.ac.uk

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Issue

Vol. 84, Iss. 5 — November 2011

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