Microscopic derivation of Open Quantum Walks

TL;DR

This paper derives Open Quantum Walks from microscopic principles, linking their dynamics to environmental thermodynamics, and demonstrates how temperature influences quantum trajectory behavior.

Contribution

It provides a microscopic derivation of both discrete and continuous Open Quantum Walks, connecting their transition operators to thermodynamic properties of the environment.

Findings

Transition between diffusive and ballistic trajectories depends on bath temperature.

Derived master equation is in the generalized form, linking dynamics to thermodynamics.

Examples include OQWs on a circle and finite chain, illustrating the theory.

Abstract

Open Quantum Walks (OQWs) are exclusively driven by dissipation and are formulated as completely positive trace preserving (CPTP) maps on underlying graphs. The microscopic derivation of discrete and continuous in time OQWs is presented. It is assumed that connected nodes are weakly interacting via a common bath. The resulting reduced master equation of the quantum walker on the lattice is in the generalised master equation form. The time discretisation of the generalised master equation leads to the OQWs formalism. The explicit form of the transition operators establishes a connection between dynamical properties of the OQWs and thermodynamical characteristics of the environment. The derivation is demonstrated for the examples of the OQW on a circle of nodes and on a finite chain of nodes. For both examples a transition between diffusive and ballistic quantum trajectories is observed and found to be related to the temperature of the bath.