Quantifying nonclassicality with local unitary operations

Sevag Gharibian
Phys. Rev. A 86, 042106 – Published 8 October 2012

Abstract

We propose a measure of nonclassical correlations in bipartite quantum states based on local unitary operations. We prove that the measure is nonzero if and only if the quantum discord is nonzero; this is achieved via a new characterization of zero discord states in terms of the state's correlation matrix. Moreover, our scheme can be extended to ensure that the same relationship holds even with a generalized version of quantum discord in which higher-rank projective measurements are allowed. We next derive a closed-form expression for our scheme in the cases of Werner states and (2×N)-dimensional systems. The latter reveals that for (2×N)-dimensional states, our measure reduces to the geometric discord [Dakić et al., Phys. Rev. Lett. 105, 190502 (2010)]. A connection to the Clauser-Horne-Shimony-Holt inequality is shown. We close with a characterization of all maximally nonclassical, yet separable, (2×N)-dimensional states of rank at most 2 (with respect to our measure).

  • Received 11 February 2012

DOI:https://doi.org/10.1103/PhysRevA.86.042106

©2012 American Physical Society

Authors & Affiliations

Sevag Gharibian

  • Institute for Quantum Computing and David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada

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Issue

Vol. 86, Iss. 4 — October 2012

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