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In a partially observed quantum or classical system the information that wecannot access results in our description of the system becoming mixed even ifwe have perfect initial knowledge. That is, if the system is quantum theconditional state will be given by a state matrix $\rho_r(t)$ and if classicalthe conditional state will be given by a probability distribution $P_r(x,t)$where $r$ is the result of the measurement. Thus to determine the evolution ofthis conditional state under continuous-in-time monitoring requires anexpensive numerical calculation. In this paper we demonstrating a numericaltechnique based on linear measurement theory that allows us to determine theconditional state using only pure states. That is, our technique reduces theproblem 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 andquantum systems as arises in modeling realistic measurement.Comment: 16 pages, 11 figure

Stochastic simulations of conditional states of partially observed systems, quantum and classical