Resource-theoretic approach to vectorial coherence

We propose a formal resource-theoretic approach to assess the coherence between partially polarized electromagnetic fields. From this framework, we identify two resource theories for the vectorial coherence: polarization-sensitive coherence and polarization-insensitive coherence. For each theory, we find the set of incoherent states and a class of operations that preserve this set (i.e., the incoherent operations). Both resource theories are endowed with a certain preorder relation that provides a hierarchy among the coherence-polarization states; thus, a necessary condition to consider in deciding whether a quantity is proper to measure the vectorial coherence is that it respects such a hierarchy. Finally, we examine most previously introduced coherence measures from this perspective.