An alternate model for protective measurements of two-level systems

Abstract

In this article we propose an alternate model for the so called {\it protective measurements}, more appropriately {\it adiabatic measurements} of a spin 1/2 system where the {\it apparatus} is also a quantum system with a {\em finite dimensional Hilbert space}. This circumvents several technical as well as conceptual issues that arise when dealing with an infinite dimensional Hilbert space as in the analysis of conventional Stern-Gerlach experiment. Here also it is demonstrated that the response of the detector is continuous and it {\it directly} measures {\em expectation values without altering the state of the system}(when the unknown original state is a {\it nondegenerate eigenstate of the system Hamiltonian}, in the limit of {\em ideal} adiabatic conditions. We have also computed the corrections arising out of the inevitable departures from ideal adiabaticity i.e the time of measurement being large but finite. To overcome the {\em conceptual} difficulties with a {\it quantum apparatus}, we have simulated a {\it classical apparatus} as a {\em large} assembly of spin-1/2 systems. We end this article with a conclusion and a discussion of some future issues.