Quantum discord and other measures of quantum correlation

Department of Physics & Astronomy Faculty of Science, Macquarie University, Australia


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 the correlations are amongst the most actively-studied topics of quantum information theory in the past decade. Entanglement is the most prominent of these correlations, but in many cases unentangled states exhibit nonclassi-cal behavior. Thus distinguishing quantum correlation 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 correlation, relate them to each other, and discuss the classical-quantum division that is common among them. In the second half, we show that the measures quantum correlation identify and quantify the deviation from classicality in various quantum information-processing tasks, quan-tum thermodynamics, open-system dynamics, and many-body physics. We show that in many cases quantum correlations indicate an advantage of quantum methods over classical ones.

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Available from: Aharon Brodutch
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    • "The two-qubit systems can demonstrate quantum correlations and these correlations correspond to entanglement phenomenon [1] or to the violation of Bell inequalities [2]. Also the correlations can be associated with quantum discord [3] [4]. The quantum discord is related to difference of classical Shannon information behavior [5] and quantum information behavior determined by von Neumann entropy of a composite bipartite systems and the entropies of its subsystems. "
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    • "It is worth emphasizing: quantum correlations relativity is not a consequence of the reference-frame change or of the more general relativistic considerations such as e.g. in [19] [20]. The degrees-of-freedom transformations implicit to our considerations cannot be written in a separable form for the unitary operators, i.e. in the form U 1 ⊗ U 2 for the 1 + 2 structure–such transformations are known to preserve discord [4] [5] [6] (and the references therein). Interestingly enough, some formally trivial variables transformations exhibit QCR also for the finite-dimensional (e.g. "

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