Projective measurements in quantum and classical optical systems

Abstract

Experimental setups for the optical implementation of projective measurements in the Laguerre-Gaussian basis are discussed. Special attention is given to the case where the measurements are made with the aid of single-mode fibers that are used to extract the Gaussian component from an optical distribution. Although this setup can, under some conditions, implement the inner product operation accurately, the overlap with the Gaussian mode in the single-mode fiber often produces cross-talk among Laguerre-Gaussian modes with different radial indices. The extent of the cross-talk is analyzed quantitatively.