Open quantum random walks formulated with quantum Bernoulli noises
Jinshu Chen, Jiahao Sun, Haoying Fu
Quantum Bernoulli noises (QBN) are the family of annihilation and creation operators acting on Bernoulli functionals, which satisfy a canonical anti-commutation relation (CAR) in equal time. This paper introduces a new type of fermionic open quantum random walk by formulating it with QBN on single-excitation subspaces. Within this framework, we establish a rigorous criterion for irreducibility, which requires the conjunction of strong graph connectivity, algebraic irreducibility of the transition operators and nonvanishing transition amplitudes. For finite irreducible walks, we prove convergence to a unique invariant state and establish strong convergence under the additional condition of aperiodicity. The theoretical framework is validated through a comprehensive two-node example, which illustrates both the convergence behavior and the intrinsic quantum features of the model.
International Journal of Modern Physics A•Feb 25, 2026•0 citations