Fig. 1: Classical models for quantum sets.
For a given set of quantum states \({\{{\rho }_{x}\}}_{x}\), we ask if it be modelled only using classical devices. a Many independent classical state-preparation devices \({{{{\mathcal{P}}}}}_{1},{{{{\mathcal{P}}}}}_{2},\ldots\) are called stochastically via a probability density function q(λ). b The classicality of \({{{{\mathcal{P}}}}}_{\lambda }\) meanse that its emitted states \({\{{\tau }_{x,\lambda }\}}_{x}\) commute, i.e. there exists a basis \({\{\left|{e}_{k}^{\lambda }\right\rangle \}}_{k}\) in which all \({\{{\tau }_{x,\lambda }\}}_{x}\) are diagonal. This is illustrated for a three-dimensional example.
