Guess your neighbor input

          @misc{ pirsa_PIRSA:11050043,
            doi = {10.48660/11050043},
            url = {https://pirsa.org/11050043},
            author = {Acin, Antonio},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Guess your neighbor input},
            publisher = {Perimeter Institute},
            year = {2011},
            month = {may},
            note = {PIRSA:11050043 see, \url{https://pirsa.org}}
          }
          

Abstract

We present “guess your neighbor input” (GYNI), a multipartite nonlocal task in which each player must guess the input received by his neighbor. We show that quantum correlations do not perform better than classical ones at this task, for any prior distribution of the inputs. There exist, however, input distributions for which general no-signalling correlations can outperform classical and quantum correlations. Some of the Bell inequalities associated to our construction correspond to facets of the local polytope. We then discuss implications of this game in connection with recent attempts of deriving quantum correlations from information based principles, such as non-trivial communication complexity, information causality and Gleason’s theorem. Our results show that truly multipartite concepts are necessary to obtain the set of quantum correlations for an arbitrary number of parties.