1202.3116 (Stephan Weis)

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

Stephan Weis

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.

View original: http://arxiv.org/abs/1202.3116