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Phys Rev E. 2016 Aug;94(2-2):026103. doi: 10.1103/PhysRevE.94.026103. Epub 2016 Aug 12.

Comment on "Quantum Kaniadakis entropy under projective measurement".

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IFLP, UNLP, CONICET, Facultad de Ciencias Exactas, Calle 115 y 49, CC 67, 1900 La Plata, Argentina.
Laboratoire Grenoblois d'Image, Parole, Signal et Automatique (GIPSA-Lab, CNRS), 11 rue des Mathématiques, 38402 Saint Martin d'Hères, France.
Dipartimento di Pedagogia, Psicologia, Filosofia, Università degli Studi di Cagliari, Cagliari, Italy.
Facultad de Matemática, Astronomía y Física (FaMAF), Universidad Nacional de Córdoba, and CONICET, Avenida Medina Allende S/N, Ciudad Universitaria, X5000HUA, Córdoba, Argentina.


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.


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