Induced metric and matrix inequalities on unitary matrices

H. F. Chau, Chi Kwong Li, Yiu Tung Poon, Nung Sing Sze

Research output: Journal article publicationJournal articleAcademic researchpeer-review

3 Citations (Scopus)

Abstract

Recently, Chau (2011 Quantum Inform. Comput. 11 721) showed that one can define certain metrics and pseudo-metrics on U(n), the group of all n × n unitary matrices, based on the arguments of the eigenvalues of the unitary matrices. More importantly, these metrics and pseudo-metrics have quantum information theoretical meanings. So it is instructive to study this kind of metrics and pseudo-metrics on U(n). Here we show that any symmetric norm on ℝ n induces a metric on U(n). Furthermore, using the same technique, we prove an inequality concerning the eigenvalues of a product of two unitary matrices which generalizes a few inequalities obtained earlier by Chau (arXiv:1006.3614v1).
Original languageEnglish
Article number095201
JournalJournal of Physics A: Mathematical and Theoretical
Volume45
Issue number9
DOIs
Publication statusPublished - 9 Mar 2012

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

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