Decoherence in one-dimensional Quantum Walk

TL;DR

This paper analyzes how decoherence affects one-dimensional quantum walks, providing generalized analytical formulas applicable to various decoherence types and illustrating with coin-position decoherence examples.

Contribution

It extends the decoherent coin quantum walk method to all decoherence types and connects with previous models, offering a comprehensive analytical framework.

Findings

Analytical expressions valid for all decoherence types

Comparison of broken line quantum walk results with numerical data

Reduction to Brun formalism for coin-only decoherence

Abstract

In this paper we study decoherence in the quantum walk on the line. We generalize the method of decoherent coin quantum walk, introduced by Brun et al [Phys. Rev. A {\bf 67}, 32304 (2003)]. Our analytical expressions are applicable for all kinds of decoherence. As an example of the coin-position decoherence, we study the broken line quantum walk and compare our results with the numerical one. We also show that our analytical results reduce to the Brun formalism when only the coin is subjected to decoherence.