An operational approach to quantum state reduction, the state change of the measured system caused by a measurement of an observable conditional upon the outcome of measurement, is founded without assuming the projection postulate in any stages of the measuring process. Whereas the conventional formula assumes that the probe measurement satisfies the projection postulate, a new formula for determining the state reduction shows that the state reduction does not depend on how the probe observable is measured, or in particular does not depend on whether the probe measurement satisfies the projection postulate or not, contrary to the longstanding attempts in showing how the macroscopic nature of probe detection provokes state reduction.
1997 Academic Press
1. Introduction
Any measurement of an observable of a microscopic system changes the state of the measured system even in the case where the projection postulate may not hold. There are two ways of describing the state change caused by a measurement. One is selective state change, or so-called state reduction, which depends on the outcome of measurement. The other is nonselective state change, which does not depend on the outcome of measurement. Since the outcome of measurement is probabilistic in quantum mechanics, state reduction is also probabilistic. The conceptual status of state reduction, as probabilistic change of state, is still polemical in measurement theory [1], whereas the concept of nonselective state change is rather straightforward.
Any measuring process consists of two stages: the first stage is the interaction between the object and the apparatus, which transduces the measured observable to the probe observable, and the second stage is the detection of the probe observable, which amplifies the probe observable to a directly sensible macroscopic variable without further disturbing the object, or which is simply the measurement of the probe observable. Nonselective state change is well described by the opensystem dynamics of the object system associated with the first stage. One of major polemical points concerning state reduction is whether the second stage plays any role in changing the state of the object dynamically.
Consider a measurement of an observable A of a quantum system S described by a Hilbert space H S . Suppose that at the time of measurement the object is in the article no. PH975706 121 0003-4916Γ97 25.00