Geometric relations in Classical and Quantum Information Theory using the Lambert-Tsallis Wq(x) function

This work presents relations using the Lambert-Tsallis function W-q(x) that provide geometric characteristics in classical and quantum information theory. Firstly, the W-q(x) function is used to estimate parameters in discrete and continuous distributions knowing the a priori probability value. A lower bound for the probability density derived from the branch point of W-q(x). Secondly, we will represent the direct relationship between the Fisher distance in theH(F)(2 )hyperbolic model of normal distributions as a function of the distance associated with the Kulback-Leibler divergence in the argument of the Lambert-Tsallis function. Subsequently, using the disentropy based on R & eacute;nyi, a functional that uses W-q(x) as its kernel, can be used as a measure of purity in the qubit state space (Bloch sphere), as well as for calculating quantum disentanglement of pure states of two qubits. Finally, representations for quantum fidelity and quantum affinity are defined as a function of W-q(x) once the Fisher and Wigner-Yanase quantum information metrics were known, connecting the Lambert-Tsallis function to the quantum speed limit (QSL) theory.

Automated summary

This work uses the Lambert-Tsallis function W-q(x) to provide geometric characteristics in classical and quantum information theory. It explores the function's applications in parameter estimation, Fisher distance, Kulback-Leibler divergence, purity measurement, and quantum disentanglement. It also connects the Lambert-Tsallis function to quantum fidelity, quantum affinity, and the quantum speed limit theory.