"This thesis identifies the model of simultaneous measurement of the position and momentum observables seminally posed by Arthurs and Kelly as a system described entirely by observables with continuous eigen spectrum; in particular, we treat the model in the regime of Gaussian states by assuming a minimum uncertainty state as the system under measurement. Under this consideration, the mathematical framework used to describe these states in quantum information processing tasks finds applicability. First, we consider the free energies of each quantum system defining the measurement setting in the measurement dynam ics; then, we study how this consideration affects the retrodictive and predictive aspects of accuracy for the simultaneous measurement of the position and momentum observables of the system under examination. We find that the accuracy of the simultaneous measurement is affected by the degree of coupling between the detectors of the measurement apparatus and the system under observation"
