ABSTRACT
In this paper, the following problem is considered: given two Hermitian matrices H and K and two real numbers x and y, determine a positive semidefinite matrix ρ such that the von Neumann entropy is maximum, subject to the condition that
and
. This question arises in information theory and in statistical mechanics in connection with the maximum-entropy inference principle. To answer it, we use this principle and numerical range methods.
Acknowledgments
The authors are grateful to the Referee for bringing ref. [Citation19] to their attention and for constructive criticisms.
Disclosure statement
No potential conflict of interest was reported by the authors.