On entropy production of repeated quantum measurements II. Examples

Abstract

We illustrate the mathematical theory of entropy production in repeated quantum measurement processes developed in a previous work by studying examples of quantum instruments displaying various interesting phenomena and singularities. We emphasize the role of the thermodynamic formalism, and give many examples of quantum instruments whose resulting probability measures on the space of infinite sequences of outcomes (shift space) do not have the (weak) Gibbs property. We also discuss physically relevant examples where the entropy production rate satisfies a large deviation principle but fails to obey the central limit theorem and the fluctuation-dissipation theorem. Throughout the analysis, we explore the connections with other, a priori unrelated topics like functions of Markov chains, hidden Markov models, matrix products and number theory.

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• On a waiting-time result of Kontoyiannis: mixing or decoupling?
• On the Ziv-Merhav theorem beyond Markovianity
• Quantum trajectory of the one atom maser
• A theory of quantum (statistical) measurement
• Quenched large deviations of Birkhoff sums along random quantum measurements
• Miniatures on Open Quantum Systems
• Asymptotic Purification of Quantum Trajectories under Random Generalized Measurements