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Quasiprobability representations of quantum theory with applications to quantum information science
 Rep. Prog. Phys. 74, 116001, 1–24 (2011); arXiv:1010.2701v3 [quantph
"... This article comprises a review of both the quasiprobability representations of infinitedimensional quantum theory (including the Wigner function) and the more recently defined quasiprobability representations of finitedimensional quantum theory. We focus on both the characteristics and applicat ..."
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This article comprises a review of both the quasiprobability representations of infinitedimensional quantum theory (including the Wigner function) and the more recently defined quasiprobability representations of finitedimensional quantum theory. We focus on both the characteristics and applications of these representations with an emphasis toward quantum information theory. We discuss the recently proposed unification of the set of possible quasiprobability representations via frame theory and then discuss the practical relevance of negativity in such representations as a criteria for quantumness. CONTENTS
The classicalquantum boundary for correlations: discord and related measures
, 2012
"... 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 amongst the more activelystudied topics of quantum information theory over the ..."
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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 amongst the more activelystudied 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 we review different notions of classical and quantum correlations quantified by quantum discord and other related measures. In the first half, we review the mathematical properties of the measures of quantum correlations, relate them to each other, and discuss the classicalquantum division that is common among them. In the second half, we show that the measures identify and quantify the deviation from classicality in various quantuminformationprocessing tasks, quantum thermodynamics, opensystem dynamics, and manybody physics. We show that in many cases quantum correlations indicate an advantage of quantum