The position-momentum uncertainty-like inequality based on moments of arbitrary order for $d$-dimensional quantum systems, which is a generalization of the celebrated Heisenberg formulation of the uncertainty principle, is improved here by use of the Rényi-entropy-based uncertainty relation. The accuracy of the resulting lower bound is physico-computationally analyzed for the two main prototypes in $d$-dimensional physics: the hydrogenic and oscillator-like systems.

We revisit generalized entropic formulations of the uncertainty principle for an arbitrary pair of quantum observables in two-dimensional Hilbert space. Rényi entropy is used as an uncertainty measure associated with the distribution probabilities corresponding to the outcomes of the observables. We derive a general expression for the tight lower bound of the sum of Rényi entropies for any couple of (positive) entropic indices (α, β). Thus, we have overcome the Hölder conjugacy constraint imposed on the entropic indices by Riesz–Thorin theorem. In addition, we present an analytical expression for the tight bound inside the square [0 , 1/2]² in the α–β plane, and a semi-analytical expression on the line β = α. It is seen that previous results are included as particular cases. Moreover we present a semi-analytical, suboptimal bound for any couple of indices. In all cases, we provide the minimizing states.

A geometric approach to formulate the uncertainty principle between quantum observables acting on an $N$-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a projector associated with an observable, and interpret it as the probability of obtaining the outcome corresponding to that projector. We make use of fidelity-based metrics such as angle, Bures, and root infidelity to propose a measure of uncertainty. The triangle inequality allows us to derive a family of uncertainty relations. In the case of the angle metric, we recover the Landau-Pollak inequality for pure states and show, in a natural way, how to extend it to the case of mixed states in arbitrary dimension. In addition, we derive and compare alternative uncertainty relations when using other known fidelity-based metrics. DOI: http://dx.doi.org/10.1103/PhysRevA.89.034101 ©2014 American Physical Society

Since the appearance in China of the first cases, the entire world has been deeply affected by the flagellum of the Coronavirus Disease (COVID-19) pandemic. There have been many mathematical approaches trying to characterize the data collected about this serious issue. One of the most important aspects for attacking a problem is knowing what information is really available. We investigate here the information contained in the COVID-19 data of infected and deceased people in all countries, using informational quantifiers such as entropy and statistical complexity. For the evaluation of these quantities, we use the Bandt–Pompe permutation methodology, as well as the wavelet transform, to obtain the corresponding probability distributions from the available series of data. The period analyzed covers from the appearance of the disease up to the massive use of anti-COVID vaccines.