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- W2099172978 abstract "We study the inverse problem of inferring the state of a finite-level quantum system from expected values of a fixed set of observables, by maximizing a continuous ranking function. We have proved earlier that the maximum-entropy inference can be a discontinuous map from the convex set of expected values to the convex set of states because the image contains states of reduced support, while this map restricts to a smooth parametrization of a Gibbsian family of fully supported states. Here we prove for arbitrary ranking functions that the inference is continuous up to boundary points. This follows from a continuity condition in terms of the openness of the restricted linear map from states to their expected values. The openness condition shows also that ranking functions with a discontinuous inference are typical. Moreover it shows that the inference is continuous in the restriction to any polytope which implies that a discontinuity belongs to the quantum domain of non-commutative observables and that a geodesic closure of a Gibbsian family equals the set of maximum-entropy states. We discuss eight descriptions of the set of maximum-entropy states with proofs of accuracy and an analysis of deviations." @default.
- W2099172978 created "2016-06-24" @default.
- W2099172978 creator A5073581559 @default.
- W2099172978 date "2014-06-20" @default.
- W2099172978 modified "2023-09-27" @default.
- W2099172978 title "Continuity of the Maximum-Entropy Inference" @default.
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- W2099172978 doi "https://doi.org/10.1007/s00220-014-2090-1" @default.
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