Continuously Diagonalized Density Operator of Open Systems

Lajos Diósi

Lajos Diósi

We showed several years ago that the density operator of Markovian open systems can be diagonalized continuously in time. The resulting pure state jump processes correspond to quantum trajectories proposed in recent quantum optics calculations or, at fundamental level, to exact consistent histories.

Ravinder Rupchand Puri

Gerard J Milburn

An analysis is presented of optical heterodyne detection of an intracavity field within the context of quantum measurement theory. We find the intracavity density operator becomes diagonal in the basis which diagonalizes the measured quantity, a quadrature phase amplitude of the field. This representation is the ``pointer basis,'' and this result is the continuous-measurement equivalent of state reduction. The model illustrates a general feature of continuous measurement; one parameter given by the product of the system and measuring device coupling bandwidth and the fluctuations in the measuring device completely characterizes the measurement. This constant determines both the rate of diagonalization of the density operator and the rate of growth of fluctuations in the system quantity conjugate to the measured observable.

J. Finkelstein

We examine the relationship between the decoherence of quantum-mechanical histories of a closed system (as discussed by Gell-Mann and Hartle) and environmentally induced diagonalization of the density operator for an open system. We study a definition of decoherence which incorporates both of these ideas, and show that it leads to a consistent probabilistic interpretation of the reduced density operator.