Limit theorems and localization of three state quantum walks on a line defined by generalized Grover coins

Abstract

In this article, we undertake a detailed study of the limiting behavior of a three-state discrete-time quantum walk on one dimensional lattice with generalized Grover coins. Two limit theorems are proved and consequently we show that the quantum walk exhibits localization at its initial position, for a wide range of coin parameters. Finally, we discuss the effect of the coin parameters on the peak velocities of probability distributions of the underlying quantum walks.

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Cited by in corpus (3)

• Using Quantum Switches to Mitigate Noise in Grover's Search Algorithm
• Coin dimensionality as a resource in quantum metrology involving discrete-time quantum walks
• Two-dimensional quantum central limit theorem by quantum walks