The role of singular values in entanglement distillation and unambiguous state discrimination

Abstract

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 (SVD) 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. We apply our result to study what states can undergo entanglement distillation in a given system.

Version 2 contains a minor revision in the abstract and a few notational corrections in the text

References in corpus (3)

• The Naimark dilated PT-symmetric brachistochrone
• Implementing general measurements on linear optical and solid-state qubits
• Resources needed for non-unitary quantum operations