Measuring the nonseparability of vector vortex beams

Vector beams have the defining property of nonseparable spatial and polarization degrees of freedom and are now routinely generated in the laboratory and used in a myriad of applications. Here we exploit the nonseparability of such beams, akin to entanglement of quantum states, to apply tools traditionally associated with quantum measurements to these classical fields. We find that the entanglement entropy is a proxy for the average degree of polarization and thus provides a single number for the vector nature of such beams. In addition to providing tools for the analysis of vector beams, we also explore the concept of classical entanglement to explain why these tools are appropriate in the first place.