Limit Theorems For the Grover Walk Without Memory

Abstract

We consider the Grover walk as a 4-state quantum walk without memory in one dimension. The walker in our 4-state quantum walk moves to the left or right. We compute the stationary distribution of the walk, in addition, we obtain the weak limit theorem

15 pages, contains an extreme open 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 (3)

• On the von Neumann and Shannon Entropies for Quantum Walks on Z^2
• Limit Theorems for Quantum Walks on the Union of Planes
• Limit Theorems for the Disordered Quantum Walk