Discrimination between States of a Quantum System by Observations

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

Let M be a von Neumann algebra with normal states φ and ω, and let αi:Ai → M be a net of positive unital mappings of finite dimensional algebras. The paper studies the existence of a net βi:M → Ai such that ω {ring operator} αi {ring operator} βi → ω and φ {ring operator} αi {ring operator} βi → φ. A necessary and sufficient condition is given for the existence of βi which may fail to hold when Ai are commutative and ω does not commute with φ. Reformulation in terms of relative entropy is given and the study of the entropic version is extended to the case when M, φ, and ω are infinite tensor products. All these mathematical problems are motivated by quantum statistical considerations.

Original languageEnglish
Pages (from-to)82-97
Number of pages16
JournalJournal of Functional Analysis
Volume120
Issue number1
DOIs
Publication statusPublished - Feb 15 1994

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Quantum Systems
Discrimination
Ring
Operator
Infinite product
Relative Entropy
Finite Dimensional Algebra
Von Neumann Algebra
Commute
Unital
Reformulation
Tensor Product
Necessary Conditions
Observation
Sufficient Conditions

ASJC Scopus subject areas

  • Analysis

Cite this

Discrimination between States of a Quantum System by Observations. / Petz, D.

In: Journal of Functional Analysis, Vol. 120, No. 1, 15.02.1994, p. 82-97.

Research output: Contribution to journalArticle

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