Comparing coherent and incoherent models for quantum homogenization

TL;DR

This paper compares coherent and incoherent quantum homogenizers, showing both can achieve state transformation with similar convergence properties, indicating coherence is not essential for thermalization modeling.

Contribution

The study introduces an incoherent quantum homogenizer and demonstrates its effectiveness, revealing that coherence is not necessary for homogenization processes.

Findings

Both homogenizers can transform any qubit state to any other with high accuracy.

Incoherent homogenizer requires similar resources as the coherent one for multiple uses.

Homogenizers are universal for repeated state transformations, with resource scaling.

Abstract

Here we investigate the role of quantum interference in the quantum homogenizer, whose convergence properties model a thermalization process. In the original quantum homogenizer protocol, a system qubit converges to the state of identical reservoir qubits through partial-swap interactions, that allow interference between reservoir qubits. We design an alternative, incoherent quantum homogenizer, where each system-reservoir interaction is moderated by a control qubit using a controlled-swap interaction. We show that our incoherent homogenizer satisfies the essential conditions for homogenization, being able to transform a qubit from any state to any other state to arbitrary accuracy, with negligible impact on the reservoir qubits' states. Our results show that the convergence properties of homogenization machines that are important for modelling thermalization are not dependent on coherence between qubits in the homogenization protocol. We then derive bounds on the resources required to re-use the homogenizers for performing state transformations. This demonstrates that both homogenizers are universal for any number of homogenizations, for an increased resource cost.