Non-multiple non-equidimensional bases and unsharp measurements

摘要

We consider a procedure of measurement of a quantum system in case when its dimension and the dimensionof the basis of a measuring device relate as ratio of integer numbers. This procedure of measurement is introducedhere as a "procedure of measurement in different-dimensional bases". We develop a new mathematical formalismdescribing this kind of measurement. It is demonstrated that when the dimension of the system is divisible by thedimension 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.