Relationship between the degree of polarization, indistinguishability, and entanglement

We address a recently established inequality P≥I that constrains the degrees of polarization P and indistinguishability I. We derive said inequality within three different frameworks, discussing its respective physical meaning. We show that in its original formulation the inequality involved a single degree of freedom, and that only by entangling polarization and path (momentum) in laboratory space, can such an inequality represent a constraint between these degrees of freedom. We show how this could be done with the help of a Mach-Zehnder-like array. We discuss this multipurpose device, which can be employed to address several issues of current interest, such as tests of the complementarity principle, partial coherence stemming from unobserved degrees of freedom, geometric phases of entangled states evolving on the Schmidt sphere, etc. Besides its experimental feasibility, the proposed device serves as a tool for studying common features of quantum and classical entangled states. In particular, it serves for testing a newly proposed measure of coherence, called Bell's measure, using experimental techniques that are independent of those already employed.