ABSTRACT
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.
ABSTRACT
We comment on the main result given by Ourabah et al. [Phys. Rev. E 92, 032114 (2015)PLEEE81539-375510.1103/PhysRevE.92.032114], noting that it can be derived as a special case of the more general study that we have provided in [Quantum Inf Process 15, 3393 (2016)10.1007/s11128-016-1329-5]. Our proof of the nondecreasing character under projective measurements of so-called generalized (h,Ï) entropies (that comprise the Kaniadakis family as a particular case) has been based on majorization and Schur-concavity arguments. As a consequence, we have obtained that this property is obviously satisfied by Kaniadakis entropy but at the same time is fulfilled by all entropies preserving majorization. In addition, we have seen that our result holds for any bistochastic map, being a projective measurement a particular case. We argue here that looking at these facts from the point of view given in [Quantum Inf Process 15, 3393 (2016)10.1007/s11128-016-1329-5] not only simplifies the demonstrations but allows for a deeper understanding of the entropic properties involved.
