A new no-go theorem for hidden variables theories

          @misc{ pirsa_PIRSA:08040073,
            doi = {10.48660/08040073},
            url = {https://pirsa.org/08040073},
            author = {Bacciagaluppi, Guido},
            keywords = {Quantum Foundations},
            language = {en},
            title = {A new no-go theorem for hidden variables theories},
            publisher = {Perimeter Institute},
            year = {2008},
            month = {apr},
            note = {PIRSA:08040073 see, \url{https://pirsa.org}}
          }
          

Abstract

Consider the quantum predictions for EPR-type measurements on two systems with Hilbert space of dimension at least 3 in any maximally entangled state. I show that the only possible hidden variables model of these probabilities that satisfies both Shimony\'s and Jarrett\'s condition of parameter independence (or `locality\') and Jones and Clifton\'s condition of conditional parameter independence (or `constrained locality\') is trivial, i.e. given by the quantum probabilities themselves. I shall attempt to discuss also the meaning of the conditions and of this result.