Quantum limits to polarization measurement of classical light

Polarization of light is one of the fundamental concepts in optics. There are many ways to measure and characterise this feature of light but at the fundamental level it is quantum mechanics that imposes ultimate limits to such measurements. Here, I calculate the quantum limit to a precision of a polarization measurement of classical coherent light. This is a multiparameter estimation problem with a crucial feature of noncommuting optimal observables corresponding to each parameter which prohibits them to be measured at the same time. I explicitly minimize the quantum Holevo-Cramer-Rao bound which tackles this issue and show that it can be locally saturated by two types of conventional receivers.