Metrics and pseudometrics on unitary groups with applications in quantum information processing
arXiv:1909.11131
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.
18 pages, 1 figure