Non-multiple non-equidimensional bases and unsharp measurements

Abstract

We consider a procedure of measurement of a quantum system in case when its dimension and the dimension of the basis of a measuring device relate as ratio of integer numbers. This procedure of measurement is introduced here as a "procedure of measurement in different-dimensional bases". We develop a new mathematical formalism describing this kind of measurement. It is demonstrated that when the dimension of the system is divisible by the dimension of basis for the measuring instrument, our results coincide with conventional theoretical developments. We consider measurement in different-dimensional bases as a kind of unsharp measurement.