Journal
IEEE TRANSACTIONS ON INFORMATION THEORY
Volume 68, Issue 1, Pages 311-321Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2021.3117440
Keywords
Testing; Tensors; Entropy; Technological innovation; Quantum channels; Optimization; Information theory; Relative submajorization; quantum resource theory; sandwiched Renyi divergence; strong converse exponent
Funding
- New National Excellence Program of the Ministry for Innovation and Technology [UNKP-19-4]
- Janos Bolyai Research Scholarship of the Hungarian Academy of Sciences
- National Research, Development and Innovation Fund of Hungary within the Quantum Technology National Excellence Program [2017-1.2.1-NKP-2017-00001]
- VILLUM FONDEN [25452]
- QMATH Centre of Excellence [10059]
- [K124152]
- [KH129601]
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In this study, we investigate quantum dichotomies and the resource theory of asymmetric distinguishability using a generalization of Strassen's theorem on preordered semirings. We find that an asymptotic variant of relative submajorization, defined on unnormalized dichotomies, can be characterized by real-valued monotones that are multiplicative under the tensor product and additive under the direct sum. These strong constraints allow us to classify and explicitly describe all such monotones, leading to a rate formula expressed as an optimization involving sandwiched Renyi divergences. As an application, we provide a new derivation of the strong converse error exponent in quantum hypothesis testing.
We study quantum dichotomies and the resource theory of asymmetric distinguishability using a generalization of Strassen's theorem on preordered semirings. We find that an asymptotic variant of relative submajorization, defined on unnormalized dichotomies, is characterized by real-valued monotones that are multiplicative under the tensor product and additive under the direct sum. These strong constraints allow us to classify and explicitly describe all such monotones, leading to a rate formula expressed as an optimization involving sandwiched Renyi divergences. As an application we give a new derivation of the strong converse error exponent in quantum hypothesis testing.
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