Metrics and pseudometrics on unitary groups with applications in quantum information processing

TL;DR

This paper develops metrics and pseudometrics on unitary groups, deriving explicit formulas and exploring their applications in quantum information processing such as distinguishability, coding, and search problems.

Contribution

It introduces new pseudometrics on unitary groups and investigates their properties and applications in quantum information tasks.

Findings

Derived explicit formulas for metrics and pseudometrics on unitary groups

Analyzed the distinguishability of unitary operators using these metrics

Applied pseudometrics to quantum coding and search problems

Abstract

Metrics and pseudometrics are defined on the group of unitary operators in a Hilbert space. Several explicit formulas are derived. A special feature of the work is investigation of pseudometrics in unitary groups. The rich classes of pseudometrics have many interesting applications. Three such applications, distinguishibility of unitary operators, quantum coding and quantum search problems are discussed.