Maximum-entropy inference and inverse continuity of the numerical range

Abstract

We study the continuity of the maximum-entropy inference map for two observables in finite dimensions. We prove that the continuity is equivalent to the strong continuity of the set-valued inverse numerical range map. This gives a continuity condition in terms of analytic eigenvalue functions which implies that discontinuities are very rare. It shows also that the continuity of the MaxEnt inference method is independent of the prior state.

15 pages, no figures, correction of v1 in Coro. 5.1 and Thm. 5.3

References in corpus (4)

• Updating Probabilities
• Information-theoretical analysis of topological entanglement entropy and multipartite correlations
• Reconstructing quantum states from local data
• Continuity of the maximum-entropy inference: Convex geometry and numerical ranges approach

Cited by in corpus (3)

• Theoretical investigations of an information geometric approach to complexity
• A new signature of quantum phase transitions from the numerical range
• Matrix systems, algebras, and open maps