Discrimination between states of a quantum system by observations
type: Item
instance of: scholarly article
title: Discrimination between states of a quantum system by observations
zbMATH Open document ID: 0808.46096
author: Dénes Petz
published in: Journal of Functional Analysis
publication date: 1995-03-09T00:00:00Z
review text: As the author points out, all mathematical problems from this paper are motivated by quantum statistical considerations. Let \(\mathcal M\) be a von Neumann algebra, and let \(\alpha_ i: {\mathcal A}_ i\to {\mathcal M}\) be a net of positive unital mappings, where \(A_ i\) is a finite-dimensional algebra. The existence of a net \(\beta_ i: M\to A_ i\) such that \(\omega\circ \alpha_ i\circ \beta_ i\to \omega\) and \(\varphi\circ \alpha_ i\circ \beta_ i\to \varphi\) is studied, where \(\omega\) and \(\varphi\) are two given normal states. The author finds a necessary and sufficient condition for the existence of \(\beta_ i\), and observes that this condition may fail when \(A_ i\) are commutative but \(\omega\) does not commute with \(\varphi\). When \({\mathcal M}\), \(\omega\), \(\varphi\), are infinite tensor products, the author gives a reformulation in terms of relative entropy.
Mathematics Subject Classification ID: 46L60
zbMATH DE Number: 599750
zbMATH Keywords: von Neumann algebra
zbMATH Keywords: net of positive unital mappings
zbMATH Keywords: normal states
zbMATH Keywords: infinite tensor products
zbMATH Keywords: relative entropy
reviewed by: Florian-Horia Vasilescu
MaRDI profile type: Publication
full work available at URL: jfan.1994.1024
OpenAlex ID: W2009322436
DOI: 10.1006/JFAN.1994.1024
description: scientific article; zbMATH DE number 599750