Bosyk, G. M.Bellomo, G.Luis Aina, Alfredo2023-06-172023-06-172018-04-010146-959210.1364/OL.43.001463https://hdl.handle.net/20.500.14352/12113© 2018 Optical Society of America. GMB and GB acknowledge CONICET (Argentina). AL acknowledges financial support from Spanish Ministerio de Economía y Competitividad Project No.FIS2016-75199-P, and from the Comunidad Autónoma de Madrid research consortium QUITEMAD+ Grant No. S2013/ICE-2801.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.engjournal articlehttp://dx.doi.org/10.1364/OL.43.001463https://www.osapublishing.orgopen access535Tensor product structuresPhase-differenceQuantum opticsDecoherenceVariablesCavityFieldsÓptica (Física)2209.19 Óptica Física