From Classical to Quantum: Uniform Continuity bounds on entropies in Infinite Dimensions
نویسندگان
چکیده
We prove a variety of improved uniform continuity bounds for entropies both classical random variables on an infinite state space and quantum states infinite-dimensional systems. obtain the first tight estimate Shannon entropy with countably alphabet. The proof relies new mean-constrained Fano-type inequality. then employ this result to derive energy-constrained bound von Neumann entropy. To deal more general in dimensions, e.g . ?-Rényi ?-Tsallis entropies, we develop novel approximation scheme based operator Hölder estimates. Finally, settle open problem raised by Shirokov [1], [2] regarding characterisation finite
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2023
ISSN: ['0018-9448', '1557-9654']
DOI: https://doi.org/10.1109/tit.2023.3248228