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In order to perform foundational experiments testing the correctness of quantum mechanics, one requires data analysis tools that do not assume quantum theory. We introduce a quantum-free tomography technique that fits experimental data to a set of states and measurement effects in a generalised probabilistic theory (GPT). (This is in contrast to quantum tomography, which fits data to sets of density operators and POVM elements.) We perform an experiment on the polarization degree of freedom of single photons, and find GPT descriptions of the states and measurements in our experiment. We gather data for a large number of preparation and measurement procedures in order to map out the spaces of allowed GPT states and measurement effects, and we bound their possible deviation from quantum theory. Our GPT tomography method allows us to bound the extent to which nature might be more or less contextual than quantum theory, as measured by the maximum achievable violation of a particular noncontextuality inequality. We find that the maximal violation is confined to lie between 1.2±0.1% less than and 1.3±0.1% greater than the quantum prediction.
Coauthors: Matthew Pusey, Robert Spekkens, Kevin Resch