A POVM view of the ensemble approach to polarization optics

TL;DR

This paper links the ensemble approach to polarization optics with POVM formalism, enabling new methods to realize Mueller devices using linear optics, bridging classical and quantum measurement theories.

Contribution

It demonstrates the formal equivalence between the ensemble approach in polarization optics and POVMs, proposing a novel way to implement Mueller devices with linear optics based on this analogy.

Findings

Derived new Mueller transformations from the ensemble formalism.

Established the formal equivalence between ensemble approach and POVMs.

Suggested practical implementation of Mueller devices using linear optics.

Abstract

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.