Quantum system structures of quantum spaces and entanglement breaking maps

Dosi A. A.

SBORNIK MATHEMATICS, vol.210, no.7, pp.928-993, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 210 Issue: 7
  • Publication Date: 2019
  • Doi Number: 10.1070/sm9074
  • Journal Name: SBORNIK MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.928-993
  • Keywords: quantum cone, quantum ball, operator systems, quantum systems, entanglement breaking mapping, UNBOUNDED OPERATORS, ALGEBRAS, QUOTIENTS, BIPOLAR, ANALOGS
  • Middle East Technical University Affiliated: Yes

Abstract

This paper is devoted to the classification of quantum systems among the quantum spaces. In the normed case we obtain a complete solution to the problem when an operator space turns out to be an operator system. The min and max quantizations of a local order are described in terms of the min and max envelopes of the related state spaces. Finally, we characterize min-max-completely positive maps between Archimedean order unit spaces and investigate entanglement breaking maps in the general setting of quantum systems.