On Optimization Problem for Positive Operator-Valued Measures
Alexander Semenovich Holevo · Lobachevskii Journal of Mathematics · 2022
It is shown that a number of optimization problems in quantum information theory: the $$\chi$$ -capacity (called the Holevo capacity in literature) of a quantum channel; the classical capacity of quantum observable; entanglement of formation—can be recast as a generalization of a Bayes problem over the set of all quantum states. This allows us to consider it as a convex programming problem for which necessary and sufficient optimality conditions along with the dual problem can be formulated.