Measurements in the L\'{e}vy quantum walk

TL;DR

This paper investigates how measurements following a Lévy waiting-time distribution affect a quantum walk, revealing sub-ballistic spreading and deriving an analytical relation for the variance exponent based on Lévy parameters.

Contribution

It introduces a novel analysis of Lévy-distributed measurements in quantum walks and derives an analytical expression for the variance exponent.

Findings

Quantum walk exhibits sub-ballistic behavior under Lévy measurements.

Derived an analytical formula linking variance exponent to Lévy distribution parameters.

Identified a transition from diffusive to sub-ballistic spreading due to Lévy measurements.

Abstract

We study the quantum walk subjected to measurements with a L\'evy waiting-time distribution. We find that the system has a sub-ballistic behavior instead of a diffusive one. We obtain an analytical expression for the exponent of the power law of the variance as a function of the characteristic parameter of the L\'evy distribution.