Analytical and probabilistic results arising from the dynamics of quantum κ-disentropy

Abstract

This work presents new analytical and probabilistic results arising from the dynamics of quantum κ-disentropy, a functional used to quantify entanglement and uses the Lambert-Kaniadakis W_κ(x) function in its kernel- a recent generalization of the Lambert W function based on the Kaniadakis κ-exponential function. First, we show how Rényi-based κ-disentropy (and consequently κ-disentropy) can be used to indicate the purity of a qubit state in the Bloch sphere. Second, we apply κ-disentropy to measure the disentanglement of two-qubit random quantum states in quantum networks, demonstrating that this functional exhibits behavior dual to the Wooters entanglement entropy formula (Wootters, W. K. Phys. Rev. Lett. 1998). Finally, we described how the quasi-probability of Fock states can be computed using the Lambert-Kaniadakis function and how the quantum relative Rényi-based κ-disentropy measures the distance between Wigner functions in phase space.