title: Comment on "Quantum Kaniadakis entropy under projective measurement".
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,ϕ) 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.
authors.affiliation: IFLP, UNLP, CONICET, Facultad de Ciencias Exactas, Calle 115 y 49, CC 67, 1900 La Plata, Argentina.
authors.forename: G M
authors.initials: GM
authors.lastname: Bosyk
authors.affiliation: Laboratoire Grenoblois d'Image, Parole, Signal et Automatique (GIPSA-Lab, CNRS), 11 rue des Mathématiques, 38402 Saint Martin d'Hères, France.
authors.forename: S
authors.initials: S
authors.lastname: Zozor
authors.affiliation: IFLP, UNLP, CONICET, Facultad de Ciencias Exactas, Calle 115 y 49, CC 67, 1900 La Plata, Argentina.|Dipartimento di Pedagogia, Psicologia, Filosofia, Università degli Studi di Cagliari, Cagliari, Italy.
authors.forename: F
authors.initials: F
authors.lastname: Holik
authors.affiliation: IFLP, UNLP, CONICET, Facultad de Ciencias Exactas, Calle 115 y 49, CC 67, 1900 La Plata, Argentina.
authors.forename: M
authors.initials: M
authors.lastname: Portesi
authors.affiliation: Facultad de Matemática, Astronomía y Física (FaMAF), Universidad Nacional de Córdoba, and CONICET, Avenida Medina Allende S/N, Ciudad Universitaria, X5000HUA, Córdoba, Argentina.
authors.forename: P W
authors.initials: PW
authors.lastname: Lamberti