Error exponent in asymmetric quantum hypothesis testing and its application to classical-quantum channel coding
By Masahito Hayashi. 2006
184 citations recorded by the source corpus.
An upper bound on simple quantum hypothesis testing in the asymmetric setting is shown using a useful inequality by Audenaert et al. [Phys. Rev. Lett. 98, 160501 (2007)] which was originally invented for symmetric setting. Using this upper bound, we obtain the Hoeffding bound, which is identical with the classical counterpart if the hypotheses, composed of two density operators, are mutually commutative. Its attainability has been a long-standing open problem. Further, using this bound, we obtain a better exponential upper bound of the average error probability of classical-quantum channel coding.
Subfields: Artificial Intelligence, Electrical and Electronic Engineering, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/81776a51429728bd4448147bdbb40d32136c090b
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In Electrical and Electronic Engineering
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Citations in the corpus
- Quantum channels and memory effects (2012, unknown): “(151) are known (Datta and Dorlas, 2007; Giovannetti, et al., 2012; Hayashi, 2007, 2009; Hayashi and Nagaoka, 2003; Holevo, 1998 b; Lloyd, 2011; Ogawa and Nagaoka, 1999, 2002; Winter, 1999 b).”
- Asymptotic Error Rates in Quantum Hypothesis Testing (2007, background): “Just as in the case of the Chernoff dista nce, the Hoeffding bound contains P i p(i) 1−s q(i) s as a sub-expression, and the quantum generalisation of the Hoeffding bound is obtained by replacing this sub-expression by Tr[ρ 1−s σ s ]. The optimality of the bound (also called the “converse part”) was”
- A Generalization of Quantum Stein’s Lemma (2009, background): “There are several distinct settings that might be considered, depending on the importance we attribute to the two types of errors [1–14].”