The role of singular values in single copy entanglement manipulations and unambiguous state discrimination

摘要

Unambiguous (non-orthogonal) state discrimination (USD) has a fundamental importance in quantum information and quantum cryptography. Various aspects of two-state and multiple-state USD are studied here using singular value decomposition of the evolution operator that describes a given state discriminating system. In particular, we relate the minimal angle between states to the ratio of the minimal and maximal singular values. This is supported by a simple geometrical picture in two-state USD. Furthermore, by studying the singular vectors population we find that the minimal angle between input vectors in multiple-state USD is always larger than the minimal angle in twostate USD in the same system. As an example we study what pure states can be probabilistically transformed into maximally entangled pure states in a given system.