Quantum discord
In quantum information theory, quantum discord is a measure of nonclassical correlations between two subsystems of a quantum system. It includes correlations that are due to quantum physical effects but do not necessarily involve quantum entanglement.
The notion of quantum discord was introduced by Harold Ollivier and Wojciech H. Zurek and, independently by L. Henderson and Vlatko Vedral. Olliver and Zurek referred to it also as a measure of quantumness of correlations. From the work of these two research groups it follows that quantum correlations can be present in certain mixed separable states; In other words, separability alone does not imply the absence of quantum correlations. The notion of quantum discord thus goes beyond the distinction which had been made earlier between entangled versus separable (non-entangled) quantum states.
In mathematical terms, quantum discord is defined in terms of the quantum mutual information. More specifically, quantum discord is the difference between two expressions which each, in the classical limit, represent the mutual information. These two expressions are:
where, in the classical case, H(A) is the information entropy, H(A, B) the joint entropy and H(A|B) the conditional entropy, and the two expressions yield identical results. In the nonclassical case, the quantum physics analogy for the three terms are used – S(ρA) the von Neumann entropy, S(ρ) the joint quantum entropy and S(ρA|ρB) a quantum generalization of conditional entropy (not to be confused with conditional quantum entropy), respectively, for probability density function ρ;
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