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

Igor Bjelakovic·Tyll Krueger·Rainer Siegmund-Schultze·Arleta Szkola
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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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Igor Bjelakovic, Tyll Krueger, Rainer Siegmund-Schultze, Arleta Szkola. 2003-02-01. Chained Typical Subspaces - a Quantum Version of Breiman's Theorem. https://arxiv.org/abs/quant-ph/0301177

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