Quantum Markov Processes

Abstract

AbstractThese notes give an introduction to some aspects of quantum Markov processes. Quantum Markov processes come into play whenever a mathematical description of irreversible time behaviour of quantum systems is aimed at. Indeed, there is hardly a book on quantum optics without having at least a chapter on quantum Markov processes. However, it is not always easy to recognize the basic concepts of probability theory in families of creation and annihilation operators on Fock space. Therefore, in these lecture notes much emphasis is put on explaining the intuition behind the mathematical machinery of classical and quantum probability. The lectures start with describing how probabilistic intuition is cast into the mathematical language of classical probability (Sects. 4.1-4.3). Later on, we show how this formulation can be extended such as to incorporate the Hilbert space formulation of quantum mechanics (Sects. 4.4,4.5). Quantum Markov processes are constructed and discussed in Sects. 4.6,4.7, and we add some further discussions and examples in Sects. 4.8-4.11.KeywordsProbability MeasureMarkov ProcessTransition OperatorConditional ExpectationStrong Operator TopologyThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.