izvuzmathИзвестия высших учебных заведений. МатематикаIzvestiya Vysshikh Uchebnykh Zavedenii. Matematika0021-34462076-4626Казанский (Приволжский) федеральный университет10.26907/0021-3446-2025-1-93-98izvuzmath-156Research ArticleСтатьиО мажоризации квантовых каналов распределениями вероятностейOn majorization of quantum channels by probability distributionsАмосовГ. Г.AmosovG. G.

Амосов Григорий Геннадьевич.

ул. Губкина, д. 8, Москва, 199911

Grigori G. Amosov.

8 Gubkina str., Moscow, 199911

gramos@mi-ras.ruМатематический институт им. В.А. Стеклова Российской академии наукРоссияSteklov Mathematical Institute of Russian Academy of SciencesRussian Federation202505022025019398Copyright © Амосов Г.Г., 20252025Амосов Г.Г.Amosov G.G.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://izvuzmath.elpub.ru/jour/article/view/156

На основе понятия мажоризации для распределения вероятностей введено определение мажоризации квантового канала распределением вероятностей. Показано, что предложенный подход позволяет решать задачу о взятии экстремумов выпуклых функций от выходных собственных значений смешанных унитарных каналов в случае, когда суммирование в определении канала ведется по группе Гейзенберга-Вейля.

Based on the concept of majorization for the probability distribution, a definition of the majorization of a quantum channel by a probability distribution is introduced. It is shown that the proposed approach makes it possible to solve the problem of taking the extremes of convex functions from the output eigenvalues of mixed unitary channels in the case when summation in the definition of the channel is carried out according to the Heisenberg-Weyl group.

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The authors declare that there are no conflicts of interest present.