Reply to “Comment on ‘Quantum Kaniadakis entropy under projective measurement’ ”

We rely on our proof of the nondecreasing character of quantum Kaniadakis entropy under projective measurement [Phys. Rev. E 92, 032114 (2015)], and we put it into perspective with the results of Bosyk et al. [Quantum Inf Process 15, 3393 (2016)]. Our method, adopted for the proof that Kaniadakis entropy does not decrease under a projective measurement, is based on Jensen's inequalities, while the method proposed by the authors of the Comment represents another alternative and clearly correct method to prove the same thing. Furthermore, we clarify that our interest in Kaniadakis entropy is due to the fact that this entropy has a transparent physical significance, emerging within the special relativity.