Discrimination between States of a Quantum System by Observations

✍ Scribed by D. Petz

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 576 KB
• Volume: 120
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1994.1024

✦ Synopsis

Let (|) be a von Neumann algebra with normal states (\varphi) and (\omega), and let (x_{1}: \alpha_{1} \rightarrow . / /) be a net of positive unital mappings of finite dimensional algebras. The paper studies the existence of a net (\beta_{i}: \mathscr{U} \rightarrow . \alpha_{i}) such that (\left(\omega, x_{i} \cdot \beta_{i} \rightarrow \omega\right.) and (\varphi: x_{i} \cdot \beta_{i} \rightarrow \varphi). A necessary and sufficient condition is given for the existence of (\beta), which may fail to hold when (\alpha_{i}) are commutative and (\omega) does not commute with (\varphi). Reformulation in terms of relative entropy is given and the study of the entropic version is extended to the case when (\mathscr{H}, \varphi), and (") are infinite tensor products. All these mathematical problems are motivated by quantum statistical considerations. '"' 1994 Academic Press, Inc.