Emergence of Randomness and Arrow of Time in Quantum Walks

TL;DR

This paper explores how randomness and the arrow of time naturally emerge in quantum walks through periodic measurements, linking quantum foundations with observable phenomena.

Contribution

It demonstrates the emergence of randomness and the arrow of time in quantum walks via periodic measurements and limit distribution analysis.

Findings

Randomness emerges from quantum walk dynamics.

Arrow of time arises through measurement processes.

Limit distribution analysis reveals fundamental quantum properties.

Abstract

Quantum walks are powerful tools not only to construct the quantum speedup algorithms but also to describe specific models in physical processes. Furthermore, the discrete time quantum walk has been experimentally realized in various setups. We apply the concept of the quantum walk to the problems in quantum foundations. We show that randomness and the arrow of time in the quantum walk gradually emerge by periodic projective measurements from the mathematically obtained limit distribution under the time scale transformation.