PIRSA:18080029

Almost quantum correlations violate the no-restriction hypothesis

Sainz, A.B. (2018). Almost quantum correlations violate the no-restriction hypothesis. Perimeter Institute. https://pirsa.org/18080029

Sainz, Ana Belen. Almost quantum correlations violate the no-restriction hypothesis. Perimeter Institute, Jul. 31, 2018, https://pirsa.org/18080029 

          @misc{ pirsa_PIRSA:18080029,
            doi = {10.48660/18080029},
            url = {https://pirsa.org/18080029},
            author = {Sainz, Ana Belen},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Almost quantum correlations violate the no-restriction hypothesis},
            publisher = {Perimeter Institute},
            year = {2018},
            month = {jul},
            note = {PIRSA:18080029 see, \url{https://pirsa.org}}
          }

Ana Belen Sainz

Gdańsk University of Technology

Talk number
PIRSA:18080029
Collection
Talk Type
Subject
Abstract
To identify which principles characterise quantum correlations, it is essential to understand in which sense this set of correlations differs from that of almost quantum correlations. We solve this problem by invoking the so-called no-restriction hypothesis, an explicit and natural axiom in many reconstructions of quantum theory stating that the set of possible measurements is the dual of the set of states. We prove that, contrary to quantum correlations, no generalised probabilistic theory satisfying the no-restriction hypothesis is able to reproduce the set of almost quantum correlations. Therefore, any theory whose correlations are exactly, or very close to, the almost quantum correlations necessarily requires a rule limiting the possible measurements. Our results suggest that the no-restriction hypothesis may play a fundamental role in singling out the set of quantum correlations among other non-signalling ones.