A POVM view of the ensemble approach to polarization optics

Statistical ensemble formalism of Kim, Mandel and Wolf (J. Opt. Soc. Am. A 4, 433 (1987)) offers a realistic model for characterizing the effect of stochastic non-image forming optical media on the state of polarization of transmittedlight. With suitable choice of the Jones ensemble, various Mueller transformations - some of which have been unknown so far - are deduced. It is observed that the ensemble approach is formally identical to the positive operator valued measures (POVM) on the quantum density matrix. This observation, in combination with the recent suggestion by Ahnert and Payne (Phys. Rev. A 71, 012330, (2005)) - in the context of generalized quantum measurement on single photon polarization states - that linear optics elements can be employed in setting up all possible POVMs, enables us to propose a way of realizing different types of Mueller devices.