Discrimination of quantum states with selected applications

Ulrike Futschik

Joonwoo Bae, L. C. Kwek

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 characterization of mutual information in cryptographic protocols, or as a technique for deriving fundamental theorems on 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 formalize information processing of physical systems such as optical communication with photons. Nevertheless, in most cases, the problems of finding 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 areas. 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.

Carles Roch i Carceller

Masashi Ban

János A. Bergou

Determining the state of a quantum system is a central task in quantum information processing since it encompasses the read-out problem. Very often the optimized state discrimination strategy is a generalized measurement (Positive Operator Valued Measure, POVM). Therefore, we begin with a brief introduction to the theory of generalized measurements and illustrate the power of the concept on examples relevant to applications in quantum cryptography.

真弓 八野, Fumiaki Shibata