Physics – Quantum Physics
Scientific paper
2005-03-31
Journal of Optics B: Quantum and Semiclassical Optics 7, S250 (2005)
Physics
Quantum Physics
16 pages, 11 figures
Scientific paper
10.1088/1464-4266/7/10/008
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 $\rho_r(t)$ and if classical the 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 of this conditional state under continuous-in-time monitoring requires an expensive numerical calculation. In this paper we demonstrating 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 as arises in modeling realistic measurement.
Gambetta Jay
Wiseman Howard M.
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