  Quantum state discrimination underlies various applications in quantum
information processing tasks. It essentially describes the distinguishability
of quantum systems in different states, and the general process of extracting
classical information from quantum systems. It is also useful in quantum
information applications, such as the characterisation of mutual information in
cryptographic protocols, or as a technique to derive fundamental theorems in
quantum foundations. It has deep connections to physical principles such as
relativistic causality. Quantum state discrimination traces a long history of
several decades, starting with the early attempts to formalise information
processing of physical systems such as optical communication with photons.
Nevertheless, in most cases, optimal strategies of quantum state discrimination
remain unsolved, and related applications are valid in some limited cases only.
The present review aims to provide an overview on quantum state discrimination,
covering some recent progress, and addressing applications in some selected
topics. This review serves to strengthen the link between results in quantum
state discrimination and quantum information applications, by showing the ways
in which the fundamental results are exploited in applications and vice versa.
