Statistical consistency of quantum-classical hybrids

TL;DR

This paper examines the limitations of quantum-classical hybrid systems, establishing a no-go theorem and showing that common approaches like mean-field and ensemble methods do not meet new statistical consistency criteria.

Contribution

It introduces a new statistical consistency requirement for quantum-classical hybrids and demonstrates its violation by existing mean-field and ensemble approaches.

Findings

Mean-field approach fails the new consistency criterion

Statistical ensemble approach also does not satisfy the requirement

Unusual features of the ensemble scheme are identified

Abstract

After formulating a no-go theorem for perfect quantum-classical hybrid systems, a new consistency requirement based on standard statistical considerations is noted. It is shown that such requirement is not fulfilled by the mean-field approach, nor by the statistical ensemble approach. Further unusual features of the latter scheme are pointed out.