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The prepare-and-measure theory is a new type of quantum paradox that revealsthe incompatibility between classical theory and quantum mechanics in terms ofthe dimensionality of physical systems.Just as the Horodecki criterion candetermine whether given quantum states are capable of exhibiting Bellnonclassicality, a similar criterion is needed for the prepare-and-measuretheory to determine whether given uantum states can exhibit theprepare-and-measure nonclassicality. Recently, Poderini et al. [Phys. Rev.Research 2, 043106 (2020)] presented such a criterion for theprepare-and-measure nonclassicality. In this work, we experimentally validatethis criterion -- 52 different sets of quantum states are prepared and testedone by one using this criterion to determine whether they can exhibit theprepare-and-measure nonclassicality, and the experimental results are in goodagreement with the theoretical expectations. The criterion experimentallyverified here has the potential to be widely used in future research on theprepare-and-measure nonclassicality.

Experimental demonstration of the criterion for the prepare-and-measure nonclassicality