The Semiring of Dichotomies and Asymptotic Relative Submajorization
Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Standard
The Semiring of Dichotomies and Asymptotic Relative Submajorization. / Perry, Christopher; Vrana, Peter; Werner, Albert H.
I: IEEE Transactions on Information Theory, Bind 68, Nr. 1, 01.01.2022, s. 311-321.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Harvard
APA
Vancouver
Author
Bibtex
}
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