Uniqueness of Poincaré beam projections

A single projective measurement on a superposition state does not provide the full information about the state. Therefore, multiple projections of the state onto a multitude of eigenstates are necessary. In this paper, we have demonstrated that generic Poincaré beams can be uniquely identified through a single projective measurement, although they are superposition states. Polarization optics utilizes different orders of Poincaré spheres as topological models to describe both uniform and spatially varying polarization states. These topological constructs quantify the underlying singularities and symmetries. Any measurement performed using a polarizer collapses the superposition state into one of its eigenstates. The additional features introduced by the orbital angular momentum basis, which vary across different orders of Poincaré spheres, make such projection measurements particularly interesting. In particular, a generic Poincaré beam exhibits the unique property that every possible superposition state produces a distinct signature intensity pattern when passed through a polarizer, a phenomenon explored in this paper.