Symmetrizing quantum dynamics beyond gossip-type algorithms

TL;DR

This paper introduces two improved dissipative methods for achieving quantum consensus, enhancing purity and enabling the preparation of symmetric states and perfect measurement correlations in multipartite quantum systems.

Contribution

It presents novel dissipative engineering techniques for quantum consensus that outperform existing algorithms in purity dynamics and enable strong measurement correlations.

Findings

Enhanced purity dynamics in quantum consensus algorithms

Ability to engineer pure Dicke states with simple controls

Guarantee of perfect measurement correlations in the consensus state

Abstract

Recently, consensus-type problems have been formulated in the quantum domain. Obtaining average quantum consensus consists in the dynamical symmetrization of a multipartite quantum system while preserving the expectation of a given global observable. In this paper, two improved ways of obtaining consensus via dissipative engineering are introduced, which employ on quasi local preparation of mixtures of symmetric pure states, and show better performance in terms of purity dynamics with respect to existing algorithms. In addition, the first method can be used in combination with simple control resources in order to engineer pure Dicke states, while the second method guarantees a stronger type of consensus, namely single-measurement consensus. This implies that outcomes of local measurements on different subsystems are perfectly correlated when consensus is achieved. Both dynamics can be randomized and are suitable for feedback implementation.