Quantum walks: decoherence and coin-flipping games

TL;DR

This paper explores how different types of decoherence affect quantum walks on a line, leading to classical behavior or retaining quantum features, and introduces new quantum games based on these effects.

Contribution

It provides analytical descriptions of how decoherence mechanisms influence quantum walk dynamics and develops new quantum game models incorporating these effects.

Findings

Decoherence via measurements causes classical diffusive behavior.

Broken links can preserve initial condition dependence in quantum walks.

Analytical equations describe all decoherence scenarios.

Abstract

We investigate the global chirality distribution of the quantum walk on the line when decoherence is introduced either through simultaneous measurements of the chirality and particle position, or as a result of broken links. The first mechanism drives the system towards a classical diffusive behavior. This is used to build new quantum games, similar to the spin-flip game. The second mechanism involves two different possibilities: (a) All the quantum walk links have the same probability of being broken. (b) Only the quantum walk links on a half-line are affected by random breakage. In case (a) the decoherence drives the system to a classical Markov process, whose master equation is equivalent to the dynamical equation of the quantum density matrix. This is not the case in (b) where the asymptotic global chirality distribution unexpectedly maintains some dependence with the initial condition. Explicit analytical equations are obtained for all cases.