Continuous Quantum Measurement of Noncommunting Observables

Quantum measurement techniques can potentially provide feedback control over quantum systems. In this work we explore the possibility of obtaining simultaneous information on two noncommuting observables defining appropriate Kraus operators acting on a quantum system. We explore several options in the form of such operators and specialize to the case of simultaneous measurement of position and momentum observables. The result of weak and strong measurements are interpolated and continuous-in-time measurement of these observables is also described. This setting departs from previous approaches in which it does not make assumptions on the nature of the measuring devices and concentrates on the mathematical form and the properties of the Kraus operator.