Chained Typical Subspaces - a Quantum Version of Breiman's Theorem

2003/01/31 by Igor Bjelaković, Igor Bjelakovic, Bjelakovic, Igor +8 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Inequalities and Applications #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #math-ph #math.DS #math.MP #math.OA #quant-ph

paper · pdf · doi:10.48550/arxiv.quant-ph/0301177

9 pages

openalex publication_date 2003/01/31 · arxiv created 2003/02/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an equivalent finitary reformulation of the classical Shannon-McMillan-Breiman theorem which has an immediate translation to the case of ergodic quantum lattice systems. This version of a quantum Breiman theorem can be derived from the proof of the quantum Shannon-McMillan theorem presented in our previous work (math.DS/0207121).

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