Quantum system structures of quantum spaces and entanglement breaking maps


Dosi A. A.

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

  • Publication Type: Article / Article
  • Volume: 210 Issue: 7
  • Publication Date: 2019
  • Doi Number: 10.1070/sm9074
  • Title of Journal : SBORNIK MATHEMATICS
  • Page Numbers: pp.928-993
  • Keywords: quantum cone, quantum ball, operator systems, quantum systems, entanglement breaking mapping, UNBOUNDED OPERATORS, ALGEBRAS, QUOTIENTS, BIPOLAR, ANALOGS

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.