Self testing in General Probabilistic Theories

          @misc{ pirsa_PIRSA:25050047,
            doi = {10.48660/25050047},
            url = {https://pirsa.org/25050047},
            author = {},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Self testing in General Probabilistic Theories},
            publisher = {Perimeter Institute},
            year = {2025},
            month = {may},
            note = {PIRSA:25050047 see, \url{https://pirsa.org}}
          }
          

Abstract

This talk will consist of two parts. In the former I discuss published work [LD, Ligthart, Gross, PRA, 2024], and in the latter some new related results. Part 1 -- Although there exist theories with "stronger bipartite entanglement" than quantum mechanics (QM), in sense that they have a larger CHSH value than Tsirelson's bound for QM, all such theories known tend to come at a cost, namely, they have strictly weaker bipartite measurements. Thus it has been conjectured that if one looks at scenarios where the correlations depend both on bipartite states and bipartite measurements, e.g. entanglement swapping, such theories cannot beat QM. However, in our recent work [LD, Ligthart, Gross, PRA, 2024], we constructed a General Probabilistic Theory (GPT) -- Oblate Stabilizer Theory (OST) -- that can both achieve a CHSH value of 4 (the mathematical maximum), and maintain this CHSH value after arbitrarily many rounds of entanglement swapping, effectively ruling out this conjecture. Part 2 -- One particularly non-intuitive feature of OST (for those in the know) is the presence of a "spurious extra dimension" in the local theory: Even though the CHSH violation involves only a two-dimensional section of local state space, we failed to make the entanglement swapping property work without going to three dimensions. In ongoing work, we managed to identify the mechanism behind this phenomenon. To this end, we have introduced a notion of self-testing for GPTs, and, using this we have established a GPT version of the "no-pancake" theorem that says that there is no completely positive map that maps the Bloch sphere to a two-dimensional section. Further, under reasonable assumptions, we have also managed to establish the uniqueness of OST, and provide a prescription for the construction of GPTs capable of stable iterated entanglement swapping.