The Semiring of Dichotomies and Asymptotic Relative Submajorization

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The Semiring of Dichotomies and Asymptotic Relative Submajorization. / Perry, Christopher; Vrana, Peter; Werner, Albert H.

In: IEEE Transactions on Information Theory, Vol. 68, No. 1, 01.01.2022, p. 311-321.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Perry, C, Vrana, P & Werner, AH 2022, 'The Semiring of Dichotomies and Asymptotic Relative Submajorization', IEEE Transactions on Information Theory, vol. 68, no. 1, pp. 311-321. https://doi.org/10.1109/TIT.2021.3117440

APA

Perry, C., Vrana, P., & Werner, A. H. (2022). The Semiring of Dichotomies and Asymptotic Relative Submajorization. IEEE Transactions on Information Theory, 68(1), 311-321. https://doi.org/10.1109/TIT.2021.3117440

Vancouver

Perry C, Vrana P, Werner AH. The Semiring of Dichotomies and Asymptotic Relative Submajorization. IEEE Transactions on Information Theory. 2022 Jan 1;68(1):311-321. https://doi.org/10.1109/TIT.2021.3117440

Author

Perry, Christopher ; Vrana, Peter ; Werner, Albert H. / The Semiring of Dichotomies and Asymptotic Relative Submajorization. In: IEEE Transactions on Information Theory. 2022 ; Vol. 68, No. 1. pp. 311-321.

Bibtex

@article{e747016bb2614e4ba3a166d0d41c1953,
title = "The Semiring of Dichotomies and Asymptotic Relative Submajorization",
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.",
keywords = "Testing, Tensors, Entropy, Technological innovation, Quantum channels, Optimization, Information theory, Relative submajorization, quantum resource theory, sandwiched Renyi divergence, strong converse exponent, QUANTUM, SPECTRUM",
author = "Christopher Perry and Peter Vrana and Werner, {Albert H.}",
year = "2022",
month = jan,
day = "1",
doi = "10.1109/TIT.2021.3117440",
language = "English",
volume = "68",
pages = "311--321",
journal = "IEEE Transactions on Information Theory",
issn = "0018-9448",
publisher = "Institute of Electrical and Electronics Engineers",
number = "1",

}

RIS

TY - JOUR

T1 - The Semiring of Dichotomies and Asymptotic Relative Submajorization

AU - Perry, Christopher

AU - Vrana, Peter

AU - Werner, Albert H.

PY - 2022/1/1

Y1 - 2022/1/1

N2 - 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.

AB - 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.

KW - Testing

KW - Tensors

KW - Entropy

KW - Technological innovation

KW - Quantum channels

KW - Optimization

KW - Information theory

KW - Relative submajorization

KW - quantum resource theory

KW - sandwiched Renyi divergence

KW - strong converse exponent

KW - QUANTUM

KW - SPECTRUM

U2 - 10.1109/TIT.2021.3117440

DO - 10.1109/TIT.2021.3117440

M3 - Journal article

VL - 68

SP - 311

EP - 321

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

SN - 0018-9448

IS - 1

ER -

ID: 316060146