arXiv:quant-ph/0411063 · Physical Review A

Continuous measurement of canonical observables and limit stochastic Schrödinger equations

John Edward Gough, Andrei Sobolev

Published Mar 17, 2004• 16 citations

Abstract

We derive the stochastic Schr\"odinger equation for the limit of continuous weak measurement where the observables monitored are canonical position and momentum. To this end we extend an argument due to Smolianov and Truman from the von Neumann model of indirect measurement of position to the Arthurs and Kelly model for simultaneous measurement of position and momentum. We require only unbiasedness of the detector states and an integrability condition sufficient to ensure a central limit effect. Despite taking a weak interaction as opposed to a weak measurement limit, the resulting stochastic wave equation is of the same form as that derived in a recent paper by Scott and Milburn for the specific case of joint Gaussian states.

DOI: 10.1103/physreva.69.032107

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