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Quantum stochastic calculus, operation valued stochastic processes and continual measurements in quantum mechanics

AIP Publishing
Journal of Mathematical Physics
Authors:
Alberto Barchielli at Politecnico di Milano
Alberto Barchielli
G. Lupieri
G. Lupieri
G. Lupieri
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Abstract

The physical idea of a continual observation on a quantum system has been recently formalized by means of the concept of operation valued stochastic process (OVSP). In this article, it is shown how the formalism of quantum stochastic calculus of Hudson and Parthasarathy allows, in a simple way, for constructing a large class of OVSP’s that in particular contains the quantum counting processes of Davies and Srinivas and continual ‘‘Gaussian’’ measurements. This result is obtained by means of a stochastic dilation of the OVSP’s: at the level of the enlarged system probabilities turn out to be expressed in terms of projection valued measures associated with certain time-dependent, commuting, self-adjoint operators.
Journal of Mathematical Physics Volume 26 issue 9 1985 [doi 10.1063_1.526851] Barchielli, A.; Lupieri, G. -- Quantum stochastic calculus, operation valued stochastic processes, and continual measu
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Journal of Mathematical Physics Volume 26 issue 9 1985 [doi 10.1063_1.526851] Barchielli, A.; Lupieri, G. -- Quantum stochastic calculus, operation valued stochastic processes, and continual measu
re.pdf
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Author content
All content in this area was uploaded by Alberto Barchielli on Jun 25, 2015
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Journal of Mathematical Physics Volume 26 issue 9 1985 [doi 10.1063_1.526851] Barchielli, A.; Lupieri, G. -- Quantum stochastic calculus, operation valued stochastic processes, and continual measu
re.pdf
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All content in this area was uploaded by Alberto Barchielli on Jun 25, 2015
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... To have no dissipation in K cl , also the compensated jump term in (47) has to vanish; then, we have also K 4 int = 0. Again, only the interaction term K 1 int , which contains H x , survives: a deterministic classical system can act only as a kind of control on the quantum system. ...
... The generator of the reduced classical dynamics takes the form (47). Semigroups like T t (59) are well known in the theory of classical stochastic processes; they are semigroups of transition probabilities of time-homogeneous Markov processes [16,17] ...
... m. We take the case of no noise: in (47) we have ...
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... Refs. [21,22,23]). It was soon realized (cf. ...
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