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arXiv · 1001.2826

Quantum stochastic differential equations and continuous measurements: unbounded coefficients

Ricardo Castro Santis·Alberto Barchielli
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Abstract

A natural formulation of the theory of quantum measurements in continuous time is based on quantum stochastic differential equations (Hudson-Parthasarathy equations). However, such a theory was developed only in the case of Hudson-Parthasarathy equations with bounded coefficients. By using some results on Hudson-Parthasarathy equations with unbounded coefficients, we are able to extend the theory of quantum continuous measurements to cases in which unbounded operators on the system space are involved. A significant example of a quantum optical system (the degenerate parametric oscillator) is shown to fulfill the hypotheses introduced in the general theory.

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Ricardo Castro Santis, Alberto Barchielli. 2010-01-18. Quantum stochastic differential equations and continuous measurements: unbounded coefficients. https://doi.org/10.1016/s0034-4877(11)80014-5

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