  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.
