A Bell inequality Analogue in quantum measure theory

          @misc{ pirsa_PIRSA:06120039,
            doi = {10.48660/06120039},
            url = {https://pirsa.org/06120039},
            author = {Henson, Joe},
            keywords = {Quantum Foundations},
            language = {en},
            title = {A Bell inequality Analogue in quantum measure theory},
            publisher = {Perimeter Institute},
            year = {2006},
            month = {dec},
            note = {PIRSA:06120039 see, \url{https://pirsa.org}}
          }
          

Abstract

In stochastic treatments of the ERRB set-up, it is equivalent to impose Bell\'s inequalities, a local causality condition, or a certain \"non-contextual hidden variables\" condition. But these conditions are violated by quantum mechanics. On the other hand, it is possible to view quantum mechanics as part of \"quantum measure theory\", a generalization of probability measure theory that allows pair wise interferences between histories whilst banning higher order interference. In this setting, is may be possible find quantum analogues of the three stochastic conditions. Following this line of inquiry, we will see that quantum measure theory allows no stronger violations of Bell\'s inequalities than does standard quantum theory. We also gain some insights into how to define causality in quantum theory.