### Abstract

Let M be a von Neumann algebra with normal states φ and ω, and let α_{i}:A_{i} → M be a net of positive unital mappings of finite dimensional algebras. The paper studies the existence of a net β_{i}:M → A_{i} such that ω {ring operator} α_{i} {ring operator} β_{i} → ω and φ {ring operator} α_{i} {ring operator} β_{i} → φ. A necessary and sufficient condition is given for the existence of β_{i} which may fail to hold when A_{i} 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 language | English |
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Pages (from-to) | 82-97 |

Number of pages | 16 |

Journal | Journal of Functional Analysis |

Volume | 120 |

Issue number | 1 |

DOIs | |

Publication status | Published - Feb 15 1994 |

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### ASJC Scopus subject areas

- Analysis

### Cite this

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

Research output: Contribution to journal › Article

*Journal of Functional Analysis*, vol. 120, no. 1, pp. 82-97. https://doi.org/10.1006/jfan.1994.1024

}

TY - JOUR

T1 - Discrimination between States of a Quantum System by Observations

AU - Petz, D.

PY - 1994/2/15

Y1 - 1994/2/15

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0040109202&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0040109202&partnerID=8YFLogxK

U2 - 10.1006/jfan.1994.1024

DO - 10.1006/jfan.1994.1024

M3 - Article

AN - SCOPUS:0040109202

VL - 120

SP - 82

EP - 97

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 1

ER -