A Quantum-Statistical Treatment of the Channel Capacity of Information Theory

Kentaro Kato, Masao Osaki, Tomohiro Suzuki +2 more

Guillaume Aubrun, Stanisław Szarek

Yasuhiro Utsumi

The performance of communication through a quantum conductor is limited by the laws of physics. The optimum channel capacity, the maximum rate at which information can be transmitted under a given signal power, i.e., the heat current, connects the theory of communication, quantum physics, and thermodynamics. Here, the author calculates the distribution of fluctuations of self-information and finds a Jarzynski equality like universal relation connecting the fluctuations of information, the R\'enyi entropy of order zero, and the optimum capacity.

Mostafa Mansour

These notes (in French) provide a concise introduction to information theory, spanning its classical foundations: Shannon entropy, joint and conditional entropies, mutual information, statistical correlations, and Markov chains; as well as Shannon's source coding and channel capacity theorems, which govern the optimal compression and transmission of information through noisy channels. They also cover the quantum extensions of these concepts, including the density operator formalism, distances between quantum states, von Neumann entropy, coherent information, conditional entropy, entanglement theory, quantum discord, and quantum resource theory.

J. P. Gordon

Alexander Semenovich Holevo

Abstract A brief general review is presented of the theory of information transmission capacities of quantum communication channels, which is a development of the classical Shannon theory. Unlike a classical communication channel, a quantum channel is characterised by a whole set of different capacities, which depend on the type of transmitted information (classical or quantum) and on additional resources used during transmission. The main characteristics of a quantum channel are considered: classical capacity, capacity assisted by entanglement between the channel input and output, quantum capacity and secret classical capacity. The unique role of the quantum entanglement property, which manifests itself, in particular, in a nonclassical phenomenon of capacity superadditivity, is emphasised.