Constructing quantum measurement processes via classical stochastic calculus

A. Barchielli and A. S. Holevo

Stochastic Processes and their Applications, 1995, vol. 58, issue 2, 293-317

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.

Keywords: 60H10; 60G35; 93E11; 81P15; Non-linear; stochastic; Schrodinger; equation; Quantum; evolution; Quantum; measuring; process; Quantum; filtering; Stochastic; differential; equations; and; changes; of; meassure (search for similar items in EconPapers)
Date: 1995
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Citations: View citations in EconPapers (4)

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