Christensen-Evans theorem and extensions of GNS-symmetric quantum Markov semigroups

2022/03/01 by Melchior Wirth, Wirth, Melchior · 3 citations
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2203.00341

openalex publication_date 2022/03/01 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

In this note we prove a refined version of the Christensen-Evans theorem for generators of uniformly continuous GNS-symmetric quantum Markov semigroups. We use this result to show the existence of GNS-symmetric extensions of GNS-symmetric quantum Markov semigroups. In particular, this implies that the generators of GNS-symmetric quantum Markov semigroups on finite-dimensional von Neumann algebra can be written in the form specified by Alicki's theorem.

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• On the existence of the KMS spectral gap in Gaussian quantum Markov semigroups
• Bimodule KMS Symmetric Quantum Markov Semigroups and Gradient Flows
• Connectivity for quantum graphs via quantum adjacency operators

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