Abstract
This brief entry gives an overview of quantum mechanics as a quantum probability theory. It begins with a review of the basic operator-algebraic elements that connect probability theory with quantum probability theory. Then quantum stochastic processes are formulated as a generalization of stochastic processes within the framework of quantum probability theory. Quantum Markov models from quantum optics are used to explicitly illustrate the underlying abstract concepts and their connections to the quantum regression theorem from quantum optics.
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Notes
- 1.
In this entry we will use the qualifier “classical” in brackets to emphasize that a theory is not quantum mechanical.
- 2.
Here we do not consider a general QSDE as we do not include the so-called gauge or exchange process Λ(t); see Hudson and Parthasarathy 1984 for details.
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Nurdin, H.I. (2021). Quantum Stochastic Processes and the Modelling of Quantum Noise. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, Cham. https://doi.org/10.1007/978-3-030-44184-5_100160
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