Measurements continuous in time and a posteriori states in quantum

Details Measurements continuous in time and a posteriori states in quantum Measurements continuous in time and a posteriori states in quantum

2005-12-22

arxiv.org/abs/quant-ph/0512189v1

J. Phys. A: Math. Gen. 24 (1991) 1495--1514

Physics

Quantum Physics

31 page. See also related papers at http://www.maths.nott.ac.uk/personal/vpb/research/mes_fou.html and http://www.maths.nott

Scientific paper

10.1088/0305-4470/24/7/022

Measurements continuous in time were consistently introduced in quantum mechanics and applications worked out, mainly in quantum optics. In this context a quantum filtering theory has been developed giving the reduced state after the measurement when a certain trajectory of the measured observables is registered (the a posteriori states). In this paper a new derivation of filtering equations is presented, in the cases of counting processes and of measurement processes of diffusive type. It is also shown that the equation for the a posteriori dynamics in the diffusive case can be obtained, by a suitable limit, from that one in the counting case. Moreover, the paper is intended to clarify the meaning of the various concepts involved and to discuss the connections among them. As an illustration of the theory, simple models are worked out.

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