Limit theorems for quantum walks driven by many coins

TL;DR

This paper establishes limit theorems for quantum walks influenced by multiple coins, revealing how initial conditions, number of coins, and time steps determine the quantum or classical nature of the particle's behavior.

Contribution

It provides rigorous results on the transition between quantum and classical behavior in quantum walks driven by many coins, highlighting the influence of initial states and coin number.

Findings

Transition from classical to quantum behavior depending on initial qubit, number of coins, and time steps

Rigorous limit theorems for quantum walks with multiple coins

Identification of conditions for quantum-classical transition in quantum walks

Abstract

We obtain some rigorous results on limit theorems for quantum walks driven by many coins introduced by Brun et al. in the long time limit. The results imply that whether the behavior of a particle is quantum or classical depends on the three factors: the initial qubit, the number of coins M, d= [t/M], where t is time step. Our main theorem shows that we can see a transition from classical behavior to quantum one for a class of three factors.