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Register a new userThe Decomposition Properties of Quantum Discord
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The quantum discord was introduced by Ollivier, Zurek, Henderson and Vedral as an indicator of the degree of quantumness of mixed states. In this paper, we give out the decomposition condition of quantum discords. Moreover, we show that under the condition, the quantum correlations between the quantum systems can be captured completely by the entanglement measure.
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We discuss some properties of the quantum discord based on the geometric distance advanced by Dakic, Vedral, and Brukner [Phys. Rev. Lett. {bf 105}, 190502 (2010)], with emphasis on Werner- and MEM-states. We ascertain just how good the measure is in representing quantum discord. We explore the dependence of quantum discord on the degree of mixedness of the bipartite states, and also its connection with non-locality as measured by the maximum violation of a Bell inequality within the CHSH scenario.
For the XXZ subclass of symmetric two-qubit X states, we study the behavior of quantum conditional entropy S_{cond} as a function of measurement angle thetain[0,pi/2]. Numerical calculations show that the function S_{cond}(theta) for X states can have at most one local extremum in the open interval from zero to pi/2 (unimodality property). If the extremum is a minimum the quantum discord displays region with variable (state-dependent) optimal measurement angle theta^*. Such theta-regions (phases, fractions) are very tiny in the space of X state parameters. We also discover the cases when the conditional entropy has a local maximum inside the interval (0,pi/2). It is remarkable that the maxima exist in surprisingly wide regions and the boundaries for such regions are defined by the same bifurcation conditions as for those with a minimum. Moreover, the found maxima can exceed the conditional entropy values at the ends of interval [0,pi/2] more than by 1%. This instils hope in the possibility to detect such maxima in experiment.
Quantum discord Q is a function of density matrix elements. The domain of such a function in the case of two-qubit system with X density matrix may consist of three subdomains at most: two ones where the quantum discord is expressed in closed analytical forms (Q_{pi/2} and Q_0) and an intermediate subdomain for which, to extract the quantum discord Q_theta, it is required to solve in general numerically a one-dimensional minimization problem to find the optimal measurement angle thetain(0,pi/2). Hence the quantum discord is given by a piecewise-analytic-numerical formula Q=min{Q_{pi/2}, Q_theta, Q_0}. Equations for determining the boundaries between these subdomains are obtained. The boundaries consist of bifurcation points. The Q_{theta} subdomains are discovered in the generalized Horodecki states, in the dynamical phase flip channel model, in the anisotropic spin systems at thermal equilibrium, in the heteronuclear dimers in an external magnetic field. We found that transitions between Q_{theta} subdomain and Q_{pi/2} and Q_0 ones occur suddenly but continuously and smoothly, i.e., nonanalyticity is hidden and can be observed in higher derivatives of discord function.
Establishing entanglement between distant parties is one of the most important problems of quantum technology, since long-distance entanglement is an essential part of such fundamental tasks as quantum cryptography or quantum teleportation. In this lecture we review basic properties of entanglement and quantum discord, and discuss recent results on entanglement distribution and the role of quantum discord therein. We also review entanglement distribution with separable states, and discuss important problems which still remain open. One such open problem is a possible advantage of indirect entanglement distribution, when compared to direct distribution protocols.
For the first time, we compute the quantum discord in bipartite systems containing up to nine qubits. An analytical expression is obtained for the discord in a bipartite system with three qubits. The dependence of the discord on the temperature and the structural parameter of the model is studied.
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