Björk, G.de Guise, H.Klimov, Andrei B.Hoz Iglesias, Pablo de laSánchez Soto, Luis Lorenzo2023-06-192023-06-192014-07-231050-294710.1103/PhysRevA.90.013830https://hdl.handle.net/20.500.14352/33947© 2014 American Physical Society. The work of G.B. is supported by the Swedish Foundation for International Cooperation in Research and Higher Education (STINT), and the Swedish Research Council (VR) through its Linnæus Center of Excellence ADOPT and Contract No. 621-2011-4575. H.d.G. is supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada. A.K. is thankful for the financial assistance of the Mexican CONACyT (Grant No. 106525). Finally, P.H. and L.L.S.S. acknowledge the support from the Spanish MINECO (Grant No. FIS2011-26786). It is also a pleasure to thank I. Bengtsson, J. J. Monzón, and G. Leuchs for stimulating discussions.We put forward an operational degree of polarization that can be extended in a natural way to fields whose wave fronts are not necessarily planar. This measure appears as a distance from a state to the set of all of its polarization-transformed counterparts. By using the Hilbert-Schmidt metric, the resulting degree is a sum of two terms: one is the purity of the state and the other can be interpreted as a classical distinguishability, which can be experimentally determined in an interferometric setup. For transverse fields, this reduces to the standard approach, whereas it allows one to get a straight expression for nonparaxial fields.engjournal articlehttp://dx.doi.org/10.1103/PhysRevA.90.013830http://journals.aps.org/open access535Hilbert-Schmidt distanceQuantum statesElectromagnetic-fieldsUnpolarized radiationStatistical distanceCorrelation-matricesRelative entropy3 dimensionsEntanglementCoherence.Óptica (Física)2209.19 Óptica Física