López-Rosa, S.; Toranzo, I. V.; Sánchez-Moreno, P.; Dehesa, J. S. Response to “Comment on “Entropy and complexity analysis of hydrogenic Rydberg atoms” [J. Math. Phys. 58, 104101 (2017)]. (English) Zbl 1373.81115 J. Math. Phys. 58, No. 10, 104102, 2 p. (2017). From the text: In their comment [J. Math. Phys. 58, No. 10, 104101, 4 p. (2017; Zbl 1373.81110)] on our paper [S. López-Rosa et al., J. Math. Phys. 54, No. 5, 052109, 18 p. (2013; Zbl 1282.81054)], L. G. Jiao and L. R. Zan argued that the expressions used for the Crámer-Rao complexity in both position and momentum spaces are incorrect due to the wrong definition of variance. Specifically they point out that: (1) the correct form of this complexity in position space is presented exactly in their work; (2) in momentum space, two different definitions of the variance are provided and corresponding Crámer-Rao complexities are discussed separately. There are two underlying issues in the Jiao-Zan comment to our paper1 which are certainly controverted, but not yet fully solved. One is the extension to arbitrary dimensions of the notion of variance of a one-dimensional probability distribution \(\rho(x)\), corresponding to some random variable \(X\) (e.g., position, momentum, …) (see, e.g. M. J. W. Hall[Phys. Rev A 59, No. 4. 2602–2615 (1999: doi:10.1103/PhysRevA.59.2602)] and A. Demboet al. [IEEE Trans. Inf. Theory 37, No. 6, 1501–1518 (1991; Zbl 0741.94001)]), that is, to a probability distribution \(\rho(\vec{r})\) of a D-dimensional observable \(\vec{r}\). Another issue is the definition of the Crámer-Rao complexity so that it approaches as close as possible the intuitive notion of complexity [L. Rudnicki et al., Phys. Lett. A 380, No. 3, 377–380 (2016; Zbl 1349.81065)]. MSC: 81P45 Quantum information, communication, networks (quantum-theoretic aspects) 94A17 Measures of information, entropy 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) Citations:Zbl 0741.94001; Zbl 1349.81065; Zbl 1373.81110; Zbl 1282.81054 PDFBibTeX XMLCite \textit{S. López-Rosa} et al., J. Math. Phys. 58, No. 10, 104102, 2 p. (2017; Zbl 1373.81115) Full Text: DOI References: [1] López-Rosa, S.; Toranzo, I. V.; Sánchez-Moreno, P.; Dehesa, J. S., Entropy and complexity analysis of hydrogenic Rydberg atoms, J. Math. Phys., 54, 052109 (2013) · Zbl 1282.81054 [2] Hall, M. J. W., Universal geometric approach to uncertainty, entropy, and information, Phys. Rev. A, 59, 2602 (1999) [3] Dembo, A.; Cover, T. M.; Thomas, J. A., Information theoretic inequalities, IEEE Trans. Inf. Theory, 37, 1501 (1991) · Zbl 0741.94001 [4] Rudnicki, L.; Toranzo, I. V.; Sánchez-Moreno, P.; Dehesa, J. S., Monotone measures of statistical complexity, Phys. Lett. A, 380, 377 (2016) · Zbl 1349.81065 [5] Dehesa, J. S.; Plastino, A. R.; Sánchez-Moreno, P.; Vignat, C., Generalized Crámer-Rao relations for non-relativistic quantum systems, Appl. Math. Lett., 25, 1689 (2012) · Zbl 1254.81033 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.