Eur. Phys. J. Special Topics 227, 1869–1883 (2019)
https://doi.org/10.1140/epjst/e2018-800119-5

Review

Open quantum walks

A mini review of the field and recent developments

¹ Quantum Research Group, School of Chemistry and Physics, University of KwaZulu-Natal, Durban, KwaZulu-Natal 4001, South Africa
² National Institute for Theoretical Physics (NITheP), KwaZulu-Natal 4001, South Africa
³ School of Electrical Engineering, KAIST, Daejeon 34141, Republic of Korea

^a e-mail: sinayskiy@ukzn.ac.za

Received: 31 July 2018
Received in final form: 13 September 2018
Published online: 31 January 2019

Abstract

Open quantum walks (OQWs) are a class of quantum walks, which are purely driven by the interaction with the dissipative environment. In this paper, we review theoretical advances on the foundations of discrete time OQWs, continuous time OQWs and a scaling limit of OQWs called open quantum Brownian motion. The main focus of the review is on the results and developments of discrete time OQW, covering general formalism, quantum trajectories for OQWs, central limit theorems, the microscopic derivation as well as possible generalisations and applications of OQWs.