The Optimization Problem of Quantum Discord In the Language of Correlated Observables
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The general zero discord condition is asymmetric in the way that it allows for conditional measurements in the complementary Hilbert space of two correlated systems. The problem of trying to see how the distribution of a certain observable changes in one Hilbert space based on the outcome of a measurement being made in the other Hilbert space however demands another projector to be introduced which removes the freedom of conditional measurements. In such a context one could show that the minimization of discord occurs along the projectors of the diagonal basis of the reduced density matrices. We present a mathematical proof of the above statement for an in general m x n separable density matrix which in turn yields an analytical expression of discord that is symmetric in expressing the quantum correlations between two systems.
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