MaximumEntropy Inference and Inverse Continuity of the Numerical Range
Abstract
We study the continuity of the maximumentropy inference map for two observables in finite dimensions. We prove that the continuity is equivalent to the strong continuity of the setvalued 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.
 Publication:

Reports on Mathematical Physics
 Pub Date:
 April 2016
 DOI:
 10.1016/S00344877(16)300222
 arXiv:
 arXiv:1502.03970
 Bibcode:
 2016RpMP...77..251W
 Keywords:

 maximumentropy inference;
 continuity;
 numerical range;
 strong continuity;
 stability;
 strong stability;
 Mathematical Physics;
 Quantum Physics;
 Primary 81P16;
 62F30;
 94A17;
 54C10;
 47A12;
 54C08;
 Secondary 47N50;
 82B26
 EPrint:
 15 pages, no figures, correction of v1 in Coro. 5.1 and Thm. 5.3