Limit Theorems for the Fibonacci Quantum Walk

Abstract

We study the discrete-time quantum walk in one-dimension governed by the Fibonacci transformation .We show localization does not occur for the Fibonacci quantum walk by investigating the stationary distribution of the walk, in addition, we obtain the weak limit theorem.

Contains an extreme problem

References in corpus (5)

• Quantum central limit theorem for continuous-time quantum walks on odd graphs in quantum probability theory
• Asymptotic evolution of quantum walks on the $N$-cycle subject to decoherence on both the coin and position degrees of freedom
• Limit Theorems For Quantum Walks Associated with Hadamard Matrices
• Quantum random walks and thermalisation
• Continuous-Time Quantum Walks on Trees in Quantum Probability Theory

Cited by in corpus (2)

• Limit Theorems for Quantum Walks on the Union of Planes
• Limit Theorems for the Disordered Quantum Walk