Comment on "Quantum Kaniadakis entropy under projective measurement"

G.M. BOSYK; STEEVE ZOZOR; F. HOLIK; MARIELA PORTESI; P.W. LAMBERTI

PHYSICAL REVIEW E - STATISTICAL PHYSICS, PLASMAS, FLUIDS AND RELATED INTERDISCIPLINARY TOPICS

American Physical Society

Lugar: New York; Año: 2016 vol. 94 p. 261031 - 261032

1063-651X

We comment on the main result given by Ourabah et al. in [Phys. Rev. E 92, 032114 (2015)], noting that it can be derived as a special case of the more general study that we have provided in [arXiv:1506.02090]. Our proof of the non-decreasing character under projective measurements of so-called generalized (h,phi)-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 [arXiv:1506.02090] not only simplifies the demonstrations but allows for a deeper understanding of the entropic properties involved.