Abstract
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.
Original language | English |
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Journal | IEEE Transactions on Information Theory |
Volume | 68 |
Issue number | 1 |
Pages (from-to) | 311-321 |
Number of pages | 11 |
ISSN | 0018-9448 |
DOIs | |
Publication status | Published - 1 Jan 2022 |
Keywords
- Testing
- Tensors
- Entropy
- Technological innovation
- Quantum channels
- Optimization
- Information theory
- Relative submajorization
- quantum resource theory
- sandwiched Renyi divergence
- strong converse exponent
- QUANTUM
- SPECTRUM