  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.
