Abstract
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.
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Funding
This work is supported by Russian Science Foundation under the grant no. 19-11-00086, https://rscf.ru/project/19-11-00086/. The author is grateful to M. E. Shirokov for useful remarks.
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(Submitted by A. M. Elizarov)
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Holevo, A.S. On Optimization Problem for Positive Operator-Valued Measures. Lobachevskii J Math 43, 1646–1650 (2022). https://doi.org/10.1134/S1995080222100158
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DOI: https://doi.org/10.1134/S1995080222100158