The classical-quantum boundary for correlations: Discord and related measures

Kavan Modi, Aharon Brodutch, Hugo Cable, Tomasz Paterek, and Vlatko Vedral
Rev. Mod. Phys. 84, 1655 – Published 26 November 2012

Abstract

One of the best signatures of nonclassicality in a quantum system is the existence of correlations that have no classical counterpart. Different methods for quantifying the quantum and classical parts of correlations are among the more actively studied topics of quantum-information theory over the past decade. Entanglement is the most prominent of these correlations, but in many cases unentangled states exhibit nonclassical behavior too. Thus distinguishing quantum correlations other than entanglement provides a better division between the quantum and classical worlds, especially when considering mixed states. Here different notions of classical and quantum correlations quantified by quantum discord and other related measures are reviewed. In the first half, the mathematical properties of the measures of quantum correlations are reviewed, related to each other, and the classical-quantum division that is common among them is discussed. In the second half, it is shown that the measures identify and quantify the deviation from classicality in various quantum-information-processing tasks, quantum thermodynamics, open-system dynamics, and many-body physics. It is shown that in many cases quantum correlations indicate an advantage of quantum methods over classical ones.

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  • Received 8 February 2012

DOI:https://doi.org/10.1103/RevModPhys.84.1655

© 2012 American Physical Society

Authors & Affiliations

Kavan Modi*

  • Department of Physics, University of Oxford, Clarendon Laboratory, Oxford, OX1 3PU, United Kingdom, and Centre for Quantum Technologies, National University of Singapore, 117543, Singapore

Aharon Brodutch

  • Department of Physics and Astronomy, Faculty of Science, Macquarie University, Sydney, NSW 2109, Australia, and Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

Hugo Cable

  • Centre for Quantum Technologies, National University of Singapore, 117543, Singapore

Tomasz Paterek

  • Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 639798, Singapore, and Centre for Quantum Technologies, National University of Singapore, 117543, Singapore

Vlatko Vedral

  • Department of Physics, University of Oxford, Clarendon Laboratory, Oxford, OX1 3PU, United Kingdom, Centre for Quantum Technologies, National University of Singapore, 117543, Singapore, and Department of Physics, National University of Singapore, 117543, Singapore

  • *kavan@quantumlah.org

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Issue

Vol. 84, Iss. 4 — October - December 2012

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