Stochastic simulations of conditional states of partially observed systems, quantum and classical
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In a partially observed quantum or classical system the information that we cannot access results in our description of the system becoming mixed, even if we have perfect initial knowledge. That is, if the system is quantum the conditional state will be given by a state matrix ?r(t), and if classical, the conditional state will be given by a probability distribution Pr(x,t), where r is the result of the measurement. Thus to determine the evolution of this conditional state, under continuous-in-time monitoring, requires a numerically expensive calculation. In this paper we demonstrate a numerical technique based on linear measurement theory that allows us to determine the conditional state using only pure states. That is, our technique reduces the problem size by a factor of N, the number of basis states for the system. Furthermore we show that our method can be applied to joint classical and quantum systems such as arise in modelling realistic (finite bandwidth, noisy) measurement.
Journal of Optics B: Quantum and semiclassical optics
Copyright 2005 Institute of Physics Publishing. This is the author-manuscript version of this paper. Reproduced in accordance with the copyright policy of the publisher.Please refer to the journal's website for access to the definitive, published version.