Generalized contextuality as a necessary resource for universal quantum computation

          @misc{ pirsa_PIRSA:24050010,
            doi = {10.48660/24050010},
            url = {https://pirsa.org/24050010},
            author = {Schmid, David},
            keywords = {Quantum Information},
            language = {en},
            title = {Generalized contextuality as a necessary resource for universal quantum computation},
            publisher = {Perimeter Institute},
            year = {2024},
            month = {may},
            note = {PIRSA:24050010 see, \url{https://pirsa.org}}
          }
          

Abstract

A universal and well-motivated notion of classicality for an operational theory is explainability by a generalized-noncontextual ontological model. I will here explain what notion of classicality this implies within the framework of generalized probabilistic theories. I then prove that for any locally tomographic theory, every such classical model is given by a complete frame representation. Using this powerful constraint on the space of possible classical representations, I will then prove that the stabilizer subtheory has a unique classical representation—namely Gross's discrete Wigner function. This provides deep insights into the relevance of Gross's representation within quantum computation. It also implies that generalized contextuality is also a necessary resource for universal quantum computation in the state injection model.