Controlling and reversing the transition from classical diffusive to quantum ballistic transport in a quantum walk by driving the coin

TL;DR

This paper demonstrates how external modulation of the coin state in a quantum walk can control and reverse the transition between classical diffusive and quantum ballistic transport, enabling reversible quantum-to-classical transitions.

Contribution

It introduces a method to control and reverse the quantum-to-classical transition in quantum walks through external coin modulation, supported by analytical and numerical evidence.

Findings

Oscillation between diffusive and ballistic spreading observed

Reversible quantum-to-classical transition demonstrated

Walker exists in a controllable mixture of classical and quantum states

Abstract

We show that the standard quantum-walk quantum-to-classical transition, characterized by ballistic-to-diffusive spreading of the walker's position, can be controlled by externally modulating the coin state. We illustrate by showing an oscillation between classical diffusive and quantum ballistic spreading using numerical and asymptotically exact closed-form solutions, and we prove that the walker is in a controllable incoherent mixture of classical and quantum walks with a reversible quantum-to-classical transition.