Continuity of the maximum-entropy inference and open projections of convex bodies

Details Continuity of the maximum-entropy inference and open projections of convex bodies Continuity of the maximum-entropy inference and open projections of convex bodies

2012-02-14

arxiv.org/abs/1202.3116v1

Physics

Quantum Physics

10 pages, 1 figure

Scientific paper

The maximum-entropy inference assigns to the mean values with respect to a fixed set of observables the unique density matrix, which is consistent with the mean values and which maximizes the von Neumann entropy. A discontinuity was recently found in this inference method for three-level quantum systems. For arbitrary finite-level quantum systems, we show that these discontinuities are no artefacts. While lying on the boundary of the set of mean values, they influence the inference of nearby mean values. We completely characterize the discontinuities by an openness condition on the linear map that assigns mean values. An example suggests that the openness condition is independent of the inference and can be formulated in terms of the convex geometry of the set of density matrices-this is left as an open problem.

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