Decoherence and classicalization of continuous-time quantum walks on graphs

TL;DR

This paper investigates how different models of decoherence affect the transition of continuous-time quantum walks on graphs from quantum to classical behavior, revealing that some models partially preserve quantum features while others fully classicalize the walk.

Contribution

It compares three decoherence models and introduces the quantum-classical dynamical distance as a metric to assess classicalization of CTQWs.

Findings

Intrinsic decoherence partially preserves quantum features.

Dephasing in the position basis fully classicalizes the walk.

Faster classicalization occurs with intrinsic decoherence and QSW models.

Abstract

We address decoherence and classicalization of continuous-time quantum walks (CTQWs) on graphs. In particular, we investigate three different models of decoherence, and employ the quantum-classical (QC) dynamical distance as a figure of merit to assess whether, and to which extent, decoherence classicalizes the CTQW, i.e. turns it into the analogue classical process. We show that the dynamics arising from intrinsic decoherence, i.e. dephasing in the energy basis, do not fully classicalize the walker and partially preserves quantum features. On the other hand, dephasing in the position basis, as described by the Haken-Strobl master equation or by the quantum stochastic walk (QSW) model, asymptotically destroys the quantumness of the walker, making it equivalent to a classical random walk. We also investigate the speed of the classicalization process, and observe a faster convergence of the QC-distance to its asymptotic value for intrinsic decoherence and the QSW models, whereas in the Haken-Strobl scenario, larger values of the decoherence rate induce localization of the walker.