From the Heisenberg to the Schr\"{o}dinger Picture: Quantum Stochastic Processes and Process Tensors

• URL: http://arxiv.org/abs/2109.09256v3
• Date: Thu, 30 Sep 2021 06:56:00 GMT
• Title: From the Heisenberg to the Schr\"{o}dinger Picture: Quantum Stochastic Processes and Process Tensors
• Authors: Hendra I. Nurdin and John E. Gough
• Abstract summary: A general theory of quantum processes was formulated by Accardi, Frigerio and Lewis in 1982. This paper gives an exposition of quantum processes and the process tensor formalism to the quantum theory of probabilistic quantum processes.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A general theory of quantum stochastic processes was formulated by Accardi, Frigerio and Lewis in 1982 within the operator-algebraic framework of quantum probability theory, as a non-commutative extension of the Kolmogorovian classical stochastic processes. More recently, studies on non-Markovian quantum processes have led to the discrete-time process tensor formalism in the Schr\"{o}dinger picture to describe the outcomes of sequential interventions on open quantum systems. However, there has been no treatment of the relationship of the process tensor formalism to the quantum probabilistic theory of quantum stochastic processes. This paper gives an exposition of quantum stochastic processes and the process tensor and the relationship between them. In particular, it is shown how the latter emerges from the former via extended correlation kernels incorporating ancillas.

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