PIRSA:06050024

Nonlocal boxes and C*-algebras

Halvorson, H. (2006). Nonlocal boxes and C*-algebras. Perimeter Institute. https://pirsa.org/06050024

Halvorson, Hans. Nonlocal boxes and C*-algebras. Perimeter Institute, May. 29, 2006, https://pirsa.org/06050024 

          @misc{ pirsa_PIRSA:06050024,
            doi = {10.48660/06050024},
            url = {https://pirsa.org/06050024},
            author = {Halvorson, Hans},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Nonlocal boxes and C*-algebras},
            publisher = {Perimeter Institute},
            year = {2006},
            month = {may},
            note = {PIRSA:06050024 see, \url{https://pirsa.org}}
          }

Hans Halvorson

Talk number PIRSA:06050024
DOI 10.48660/06050024
Collection
Talk Type Scientific Series
Subject

Abstract

Clifton, Bub, and Halvorson claim to be able to derive quantum mechanics from information-theoretic axioms. However, their derivation relies on the auxiliary assumption that the relevant probabilities for measurement outcomes can be represented by the observables (self-adjoint operators) and states of a C*-algebra. There are legitimate probability theories that are not so representable --- in particular, the nonlocal boxes of Popescu and Rohrlich. We explain the impact of nonlocal boxes on the interpretation of the CBH derivation, and we discuss possible generalizations of the CBH derivation in the framework of these more general probability theories.