General formulas for capacity of classical-quantum channels

By Masahito Hayashi, H. Nagaoka. IEEE Transactions on Information Theory, 2002

342 citations recorded by the source corpus.

The capacity of a classical-quantum channel (or, in other words, the classical capacity of a quantum channel) is considered in the most general setting, where no structural assumptions such as the stationary memoryless property are made on a channel. A capacity formula as well as a characterization of the strong converse property is given just in parallel with the corresponding classical results of Verdu-Han (1994) which are based on the so-called information-spectrum method. The general results are applied to the stationary memoryless case with or without cost constraint on inputs, whereby a deep relation between the channel coding theory and the hypothesis testing for two quantum states is elucidated.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/b8daed17391c24a0476da685833b9cbb39df36fa

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Citations in the corpus

Quantum channels and memory effects (2012, methodology): “As a matter of fact, strong converse coding theorems have been derived only a for limited classes of finite dimensional channels (König and Wehner, 2009; Ogawa and Nagaoka, 1999; Wilde, Winter, and Yang, 2013; Winter, 1999 b) while explicit counter-examples have been provided which show that in gen”
Information Spectrum Approach to Second-Order Coding Rate in Channel Coding (2008, methodology): “Theorem 6: (Verdú & Han[14], Hayashi & Nagaoka [15]) The relations Cp(R|W ) = inf P lim γ↓0 Ip(R − γ|P ,W ) = inf P sup Q lim γ↓0 Jp(R− γ|P ,Q,W ) (39) C(ǫ|W ) = sup P I(ǫ|P ,W ) = sup P inf Q J(ǫ|P ,Q,W ) (40)”
Min- and Max-Relative Entropies and a New Entanglement Monotone (2008, background): “Note that the above definitions of the spectral divergence rates differ slightly from those originally given in (38) and (39) of [13].”
Error exponent in asymmetric quantum hypothesis testing and its application to classical-quantum channel coding (2006, methodology): “Then, the inequality (44) in Hayashi-Nagaoka[4] mentioned that for any distribution p and any test T (n), there exists a code Φ(n) with the size N whose average error probability Pe(Φ (n)) satisfies Pe(Φ (n)) ≤ 2(1 − TrR⊗nT (n)) + 4NTrS⊗nT (n).”
Quantum channels with memory (2005, methodology): “A completely diﬀerent approach has been taken by Hayashi and Nagaoka [23], who refrain from imposing any structural assumption on the quantum channels they consider, and apply the information-spectrum method to obtain a coding theorem for the classical product state capacity, following work by…”
A Survey on Quantum Channel Capacities (2018, background): “4) Quantum Channels: About the statistical properties of the HSW theory and the general HSW capacity, a very interesting paper was published by Hayashi and Nagaoka in 2003 [218].”