Jay Gambetta and H M Wiseman 2005 J. Opt. B: Quantum Semiclass. Opt. 7 S250 doi:10.1088/1464-4266/7/10/008
Jay Gambetta1 and H M Wiseman2
Show affiliationsIn 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 ρr(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.
42.50.Ar Photon statistics and coherence theory
03.65.Ta Foundations of quantum mechanics; measurement theory
03.65.Yz Decoherence; open systems; quantum statistical methods
Issue 10 (October 2005)
Received 31 March 2005, accepted for publication 9 June 2005
Published 14 September 2005
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