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Constructing quantum measurement processes via classical stochastic calculus

Author

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  • Barchielli, A.
  • Holevo, A. S.

Abstract

A class of linear stochastic differential equations in Hilbert spaces is studied, which allows to construct probability densities and to generate changes in the probability measure one started with. Related linear equations for trace-class operators are discussed. Moreover, some analogue of filtering theory gives rise to related non-linear stochastic differential equations in Hilbert spaces and in the space of trace-class operators. Finally, it is shown how all these equations represent a new formulation and a generalization of the theory of measurements continuous in time in quantum mechanics.

Suggested Citation

  • Barchielli, A. & Holevo, A. S., 1995. "Constructing quantum measurement processes via classical stochastic calculus," Stochastic Processes and their Applications, Elsevier, vol. 58(2), pages 293-317, August.
    • Handle: RePEc:eee:spapps:v:58:y:1995:i:2:p:293-317
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    Cited by:

    1. Brecht Donvil & Paolo Muratore-Ginanneschi, 2022. "Quantum trajectory framework for general time-local master equations," Nature Communications, Nature, vol. 13(1), pages 1-11, December.
    2. Barchielli, A. & Paganoni, A. M. & Zucca, F., 1998. "On stochastic differential equations and semigroups of probability operators in quantum probability," Stochastic Processes and their Applications, Elsevier, vol. 73(1), pages 69-86, January.
    3. Pellegrini, Clément, 2010. "Existence, uniqueness and approximation of the jump-type stochastic Schrodinger equation for two-level systems," Stochastic Processes and their Applications, Elsevier, vol. 120(9), pages 1722-1747, August.
    4. Lu Zhang & Caishi Wang & Jinshu Chen, 2023. "Interacting Stochastic Schrödinger Equation," Mathematics, MDPI, vol. 11(6), pages 1-16, March.

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