Specker's parable of the overprotective seer: Implications for Contextuality, Nonlocality and Complementarity

          @misc{ pirsa_PIRSA:10100060,
            doi = {10.48660/10100060},
            url = {https://pirsa.org/10100060},
            author = {Spekkens, Robert},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Specker{\textquoteright}s parable of the overprotective seer: Implications for Contextuality, Nonlocality and Complementarity},
            publisher = {Perimeter Institute},
            year = {2010},
            month = {oct},
            note = {PIRSA:10100060 see, \url{https://pirsa.org}}
          }
          

Abstract

I revisit an example of stronger-than-quantum correlations that was discovered by Ernst Specker in 1960. The example was introduced as a parable wherein an over-protective seer sets a simple prediction task to his daughter's suitors. The challenge cannot be met because the seer asks the suitors for a noncontextual assignment of values but measures a system for which the statistics are inconsistent with such an assignment. I will show how by generalizing these sorts of correlations, one is led naturally to some well-known proofs of nonlocality and contextuality, and to some new ones. Specker's parable involves a kind of complementarity that does not arise in quantum theory - three measurements that can be implemented jointly pairwise but not triplewise -- and therefore prompts the question of what sorts of foundational principles might rule out this kind of complementarity. This is joint work with Howard Wiseman and Yeong-Cherng Liang.