Digitized continuous quantum trajectory

Abstract

In continuous measurement, we never have empirical access to the true continuous signal, but rather, to a digitized (discretized) average of the true signal over a finite number time bins. If these time bins are really much smaller than all other time scales, one can reconstruct the quantum trajectory naively with an Euler scheme. Even then, it is just a (good) approximation that cannot be refined. Can one do better? I'll show that one can define a quantum state conditioned on the binned signal (i.e. on a finite list of signal averages), and that, quite surprisingly, this binned conditional state can be efficiently reconstructed. This allows more accurate (in the Bayesian sense) reconstruction of quantum trajectories from data, and can also be used for sampling of trajectories.