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      Quantum discord and geometry for a class of two-qubit states

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          Abstract

          We study the level surfaces of quantum discord for a class of two-qubit states with parallel nonzero Bloch vectors. The dynamic behavior of quantum discord under decoherence is investigated. It is shown that a class of X states has sudden transition between classical and quantum correlations under decoherence. Our results include the ones in M. D. Lang and C. M. Caves [Phys. Rev. Lett. 105, 150501 (2010)] as a special case and show new pictures and structures of quantum discord.

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          Quantum entanglement

          Ryszard Horodecki, Karol Horodecki, Pawel Horodecki … (2007)
          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.
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            Entanglement of Formation of an Arbitrary State of Two Qubits

            William Wootters (1997)
            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.
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              Introducing Quantum Discord

              David Hedin, Gerald Blazey, Arnaud Duperrin … (2013)
              Two classically identical expressions for the mutual information generally differ when the two systems involved are quantum. We investigate this difference -- quantum discord -- and show that it can be used as a criterion for the classicality of the correlations. We also show that quantum discord can be used for describing the selection of the preferred, effectively classical, pointer states.
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                Author and article information

                Journal
                Publication date Created: 11 April 2011
                Article
                DOI: 10.1103/PhysRevA.83.022321
                ArXiV ID: 1104.1843
                SO-VID: e590c3e9-b8a4-44f2-b492-50697c6d0641
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                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Journal reference Physical Review A 83, 022321(2011)
                Comments 5 pages, 5 figures
                Categories quant-ph

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