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

TL;DR

This paper explores how singular values influence unambiguous state discrimination and entanglement distillation, providing geometric insights and linking minimal angles between states to singular value ratios.

Contribution

It introduces a novel approach using singular value decomposition to analyze state discrimination and entanglement distillation in quantum systems.

Findings

Minimal angle between states relates to singular value ratios.

Geometrical interpretation of two-state USD.

Conditions for entanglement distillation based on singular values.

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.