Speaker
Description
Since the first years of the 20th century, classical Markov chains have been a standard theoretical tool to model the statistics of a huge plethora of phenomena in physics, economics, biology, etc. Also, they are intensively used for Monte Carlo simulations [1]. The mathematical properties of these stochastic processes have been still studied over the last years because of their broad interest [2].
In this talk we will focus our attention on quantum Markov chains, the quantum counterpart of classical ones, commonly used in quantum information theory but also employed to describe neural networks [3]. Specifically, we will discuss known and new results about the asymptotics of these chains [4], comparing them with the analogous findings in the classical setting.
Joint work with P. Facchi and A. Konderak.
References:
[1] S. Brooks, J. R. Stat. Soc., 47 69 (1998);
[2] F. Fidaleo, and E. Vincenzi, Stochastics, 1 (2022);
[3] M. Lewenstein et al., Quantum Sci. Technol., 6 045002 (2021) ;
[4] D. Amato et al., arXiv:2210.17513 [quant-ph] (2022).
