We construct a universal code for a stationary and memoryless classical-quantum channel as a quantum version of the universal coding by Csiszár and Körner. Our code is constructed utilizing a combination of irreducible representations, a decoder introduced through the quantum information spectrum, and the packing lemma.
We derive universal classical-quantum superposition coding and universal classical-quantum multiple access channel code by using generalized packing lemmas for the type method. Using our classical-quantum universal superposition code, we establish the capacity region of a classical-quantum compound broadcast channel with degraded message sets. Our universal classical-quantum multiple access channel codes have two types of codes. One is a code with joint decoding and the other is a code with separate decoding. It is not so easy to construct a former code that universally achieves general points of the capacity region beyond corner points. First, we construct the latter code that universally achieves general points of the capacity region. Then, converting the latter code to the former code, we construct the above desired code with the former type. A full version of this paper is accessible at http://arxiv.org/abs/2011.00410
We derive universal classical-quantum superposition coding and universal classical-quantum multiple access channel coding by using generalized packing lemmas for the type method. Using our classical-quantum universal superposition code, we establish the capacity region of a classical-quantum compound broadcast channel with degraded message sets. Our universal classical-quantum multiple access channel codes have two types of codes. One is a code with joint decoding and the other is a code with separate decoding. It is not so easy to construct a former code that universally achieves general points of the capacity region beyond corner points. First, we construct the latter code that universally achieves general points of the capacity region. Then, converting the latter code to the former coder, we construct the above desired code with the former type.
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.
In this paper, we consider the transmission of classical information through a class of quantum channels with long-term memory, which are convex combinations of memoryless channels. Hence, the memory of such channels can be considered to be given by a Markov chain which is aperiodic but not irreducible. We prove the coding theorem and weak converse for this class of channels. The main techniques that we employ are a quantum version of Feinstein's fundamental lemma (Feinstein A 1954 IRE Trans. PGIT 4 2–22, Khinchin A I 1957 Mathematical Foundations of Information Theory: II. On the Fundamental Theorems of Information Theory (New York: Dover) chapter IV) and a generalization of Helstrom's theorem (Helstrom C W 1976 Quantum detection and estimation theory Mathematics in Science and Engineering vol 123 (London: Academic)).
We address the problem of constructing fully universal private channel coding protocols for classical-quantum (c-q) channels. Previous work constructed universal decoding strategies, but the encoder relied on random coding, which prevents fully universal code construction. In this work, we resolve this gap by identifying an explicit structural property of codebooks -- namely, the spectral expansion of an associated Schreier graph -- that guarantees universal channel resolvability. Our analysis reveals how this property can be related to channel resolvability through the theory of induced representation. Our main technical result shows that when the transition matrix of a graph associated with a codebook has a large spectral gap, the channel output induced by uniformly sampled codewords is asymptotically indistinguishable from the target output distribution, independently of the channel. This establishes the first deterministic, channel-independent construction of resolvability codebooks. Building on this, we construct a fully universal private channel coding protocol by combining it with universal c-q channel coding based on the Schur-Weyl duality. With appropriate modifications to the requirements on codebooks of universal c-q channel coding, we show that our fully universal private channel coding achieves the known optimal rate. This work thus sheds new light on the expander property of a graph in the context of secure communication.
Constructing optimal quantum information protocols without complete knowledge of the underlying states or channels is a central challenge. We address this challenge by developing universal correlation detection as a common building block for quantum communication. Our detectors distinguish a bipartite state from the product of its marginals and attain the same first-order asymptotic performance as optimal tests constructed with complete state information. For general bipartite quantum states, knowledge of a single marginal suffices: a detector depending only on that marginal is first-order optimal for every compatible state. For classical-quantum states, the detector is fully universal and requires no prior state information. By combining these detectors with position-based decoding and convex splitting, we construct channel-independent coding schemes that achieve capacity for a range of communication tasks. These results turn universal correlation detection into a systematic tool for universal protocol design, providing a unified route to designing capacity-achieving protocols for many communication tasks over unknown quantum channels.