Geodesic
On Jensen Gap and Capacity of a Shifted Depolarizing Quantum Channel
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Noncommutative Analysis and Quantum Information Theory, Tome 324 (2024), pp. 39-50

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We study the problem of maximizing the Jensen gap with respect to the probability distribution in a fairly general case, and prove a theorem on the optimal distribution. Using the results obtained, we calculate the one-shot capacity of a certain family of non-unital quantum channels. We show that in sufficiently large dimensions the channel admits one of two modes of an optimal input ensemble depending on the parameters. We also prove that both the fulfillment and the violation of the entanglement-breaking property are possible in any dimension depending on the parameters of the channel.
Keywords: quantum communication channel, shifted depolarizing channel, channel capacity. 
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     author = {E. L. Baitenov},
     title = {On {Jensen} {Gap} and {Capacity} of a {Shifted} {Depolarizing} {Quantum} {Channel}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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E. L. Baitenov. On Jensen Gap and Capacity of a Shifted Depolarizing Quantum Channel. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Noncommutative Analysis and Quantum Information Theory, Tome 324 (2024), pp. 39-50. http://geodesic.mathdoc.fr/item/TM_2024_324_a3/