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Some Continuity Properties of Quantum Rényi Divergences

Mosonyi, Milan ; Hiai, Fumio

IEEE transactions on information theory, 2024-04, Vol.70 (4), p.2674-2700 [Periódico revisado por pares]

IEEE

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Título:
Some Continuity Properties of Quantum Rényi Divergences
Autor: Mosonyi, Milan ; Hiai, Fumio
Assuntos: Atmospheric measurements ; channel discrimination ; Entropy ; Error probability ; Hilbert space ; maximal Rényi divergences ; measured Rényi divergences ; Particle measurements ; quantum channel divergences ; Quantum channels ; Quantum Rényi divergences ; relative entropy ; strong converse ; Task analysis
É parte de: IEEE transactions on information theory, 2024-04, Vol.70 (4), p.2674-2700
Descrição: In the problem of binary quantum channel discrimination with product inputs, the supremum of all type II error exponents for which the optimal type I errors go to zero is equal to the Umegaki channel relative entropy, while the infimum of all type II error exponents for which the optimal type I errors go to one is equal to the infimum of the sandwiched channel Rényi <inline-formula> <tex-math notation="LaTeX">\alpha </tex-math></inline-formula>-divergences over all <inline-formula> <tex-math notation="LaTeX">\alpha >1 </tex-math></inline-formula>. We prove the equality of these two threshold values (and therefore the strong converse property for this problem) using a minimax argument based on a newly established continuity property of the sandwiched Rényi divergences. Motivated by this, we give a detailed analysis of the continuity properties of various other quantum (channel) Rényi divergences, which may be of independent interest.
Editor: IEEE
Idioma: Inglês

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Some Continuity Properties of Quantum Rényi Divergences

Mosonyi, Milan ; Hiai, Fumio

IEEE

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