Studies on the generalized elephant quantum walk - Naves, Caio Botelho (2022)
Quantum walks have been a platform for the study and modeling of many processes and physical systems, going from its application on the development of quantum algorithms to the study of energy transport in biological molecules. In the same way that in general aspects of quantum theory, it also aroused the necessity of studying the introduction of noise in the evolution of quantum walks, given that it is a major factor in experimental applications. In this context, in 2018 G. D. Molfetta et al. presented a quantum model of the classical elephant random walk, the elephant quantum walk, that analyzes a noisy unitary evolution. Posteriorly, M. A. Pires et al. generalized this walk into the generalized elephant quantum walk, showing to have an interesting property of controlling the diffusive behavior of the walker while maintaining the maximum generation of entanglement between its degrees of freedom, something unknown until then. In this work we proposed ourselves to study, through numerical experiments, the generation of entanglement in the generalized elephant quantum walk in general initial settings and evolutions. For such, first we introduce classical random walks, reviewing the necessary probability concepts. After, we approach quantum walks and restrict the description to coined discrete time quantum walks, the type of quantum walk to be studied. Our results indicate that this type of quantum walk potentially generates maximally entangled states for almost all initial states and evolutions, even with a low degree of noise. These results indicate that a dynamically random evolution, being it either in the coin operator, as previously studied for other authors, or in the shift operator as in this walk, generates maximally correlated states.