74
views
0
recommends
+1 Recommend
0 collections
    4
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

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

      Preprint
      , , , ,

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          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 amongst 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 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 classical-quantum division that is common among them. In the second half, we show 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. We show that in many cases quantum correlations indicate an advantage of quantum methods over classical ones.

          Related collections

          Most cited references35

          • Record: found
          • Abstract: found
          • Article: found
          Is Open Access

          Quantum entanglement

          All our former experience with application of quantum theory seems to say: {\it what is predicted by quantum formalism must occur in laboratory}. But the essence of quantum formalism - entanglement, recognized by Einstein, Podolsky, Rosen and Schr\"odinger - waited over 70 years to enter to laboratories as a new resource as real as energy. This holistic property of compound quantum systems, which involves nonclassical correlations between subsystems, is a potential for many quantum processes, including ``canonical'' ones: quantum cryptography, quantum teleportation and dense coding. However, it appeared that this new resource is very complex and difficult to detect. Being usually fragile to environment, it is robust against conceptual and mathematical tools, the task of which is to decipher its rich structure. This article reviews basic aspects of entanglement including its characterization, detection, distillation and quantifying. In particular, the authors discuss various manifestations of entanglement via Bell inequalities, entropic inequalities, entanglement witnesses, quantum cryptography and point out some interrelations. They also discuss a basic role of entanglement in quantum communication within distant labs paradigm and stress some peculiarities such as irreversibility of entanglement manipulations including its extremal form - bound entanglement phenomenon. A basic role of entanglement witnesses in detection of entanglement is emphasized.
            Bookmark
            • Record: found
            • Abstract: found
            • Article: found
            Is Open Access

            Entanglement of Formation of an Arbitrary State of Two Qubits

            The entanglement of a pure state of a pair of quantum systems is defined as the entropy of either member of the pair. The entanglement of formation of a mixed state is defined as the minimum average entanglement of an ensemble of pure states that represents the given mixed state. An earlier paper [Phys. Rev. Lett. 78, 5022 (1997)] conjectured an explicit formula for the entanglement of formation of a pair of binary quantum objects (qubits) as a function of their density matrix, and proved the formula to be true for a special class of mixed states. The present paper extends the proof to arbitrary states of this system and shows how to construct entanglement-minimizing pure-state decompositions.
              Bookmark
              • Record: found
              • Abstract: not found
              • Article: not found

              Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states

                Bookmark

                Author and article information

                Journal
                29 December 2011
                2012-11-27
                Article
                10.1103/RevModPhys.84.1655
                1112.6238
                c5f73297-79bd-486d-9e28-13e4d593350c

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                Rev. Mod. Phys. 84, 1655-1707 (2012)
                Close to the published version
                quant-ph cond-mat.stat-mech math-ph math.MP

                Comments

                Comment on this article