An alternate model for protective measurements of two-level systems.
Anirban Das, Indian Institute of Technology
We propose an alternate model for the
so called protective measurements, more appropriately
adiabatic measurements of a spin 1/2 system where the
apparatus is also a quantum system with a 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 directly
measures expectation values without altering the state
of the system(when the unknown original state is a nondegenerate eigenstate of the system Hamiltonian, in the limit of 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 conceptual difficulties with a quantum apparatus, we have simulated a classical apparatus as a large assembly of spin-1/2 systems. We end this article with a conclusion and a discussion of some future issues.
