Abstract
Quantum discord measures quantum correlation by comparing the quantum mutual information with the maximal amount of mutual information accessible to a quantum measurement. This paper analyzes the properties of diagonal discord, a simplified version of discord that compares quantum mutual information with the mutual information revealed by a measurement that correspond to the eigenstates of the local density matrices. In contrast to the optimized discord, diagonal discord is easily computable; it also finds connections to thermodynamics and resource theory. Here we further show that, for the generic case of non-degenerate local density matrices, diagonal discord exhibits desirable properties as a preferable discord measure. We employ the theory of resource destroying maps (Liu Z-W et al 2017 Phys. Rev. Lett. 118 060502) to prove that diagonal discord is monotonically nonincreasing under the operation of local discord nongenerating qudit channels, d > 2, and provide numerical evidence that such monotonicity holds for qubit channels as well. We also show that it is continuous, and derive a Fannes-like continuity bound. Our results hold for a variety of simple discord measures generalized from diagonal discord.
Highlights
Quantum discord measures a very general form of non-classical correlation, which can be present in quantum systems even in the absence of entanglement
This paper analyzes the properties of diagonal discord, a simplified version of discord that compares quantum mutual information with the mutual information revealed by a measurement that correspond to the eigenstates of the local density matrices
We show that local isotropic channels, a subset of commutativity-preserving maps, commute with the canonical discord destroying map, which implies that diagonal discord is monotone under them by [24]
Summary
Quantum discord measures a very general form of non-classical correlation, which can be present in quantum systems even in the absence of entanglement. The canonical version of discord is defined to be the difference between quantum mutual information (total correlation) and the maximum amount of correlation that is locally accessible (classical correlation), which involves optimization over all possible local measurements. Such optimization renders the problem of studying discord and its variants (such as quantum deficit [9], geometric discord [10]) very difficult. It should be emphasized that diagonal discord should just be seen as a different way of measuring the same type of resource, which correspond to different operational and physical meanings In this sense, it is not very meaningful to directly compare the values of diagonal discord and optimized discord
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