On parameter estimation for quantum processes

Summary form only given, as follows. A comparative discussion of three basic procedures of continuous quantum measurement for estimating parameters of quantum stochastic processes is presented. Quantum stochastic process is one-parameter family of (vector) operators in a Hilbert space, together with a density operator, defining quantum state. If the density operator depends on unknown parameters, one may speak of the parameter estimation from quantum measurements of the process. The fundamental difficulty of the quantum case is that components of the process may not commute, and a measurement at some time will introduce specific quantum disturbances at later times. Its resolution requires the new concept of quantum measurement, continuous in time. Three basic procedures are described: quantum nondemolition (QND), quantum demolition (QD), and extended quantum nondemolition (EQND) measurements. It is shown that statistical inference based on QND and QD leads to estimates which are in general only suboptimal, while EQND reaches fundamental limitations imposed by the quantum Cramer-Rao inequality. The argument is based on physically motivated examples and leads to possible implementation of the discussed measurement procedures