Depicting Non-locality

          @misc{ pirsa_PIRSA:12040100,
            doi = {10.48660/12040100},
            url = {https://pirsa.org/12040100},
            author = {Coecke, Bob},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Depicting Non-locality},
            publisher = {Perimeter Institute},
            year = {2012},
            month = {apr},
            note = {PIRSA:12040100 see, \url{https://pirsa.org}}
          }
          

Abstract

We establish a tight relationship between two key quantum theoretical notions: non-locality and complementarity. In particular, we establish a direct connection between Mermin-type non-locality scenarios, which we generalise to an arbitrary number of parties, using systems of arbitrary dimension, and performing arbitrary measurements, and a new stronger notion of complementarity which we introduce here.    Our derivation of the fact that strong complementarity is a necessary condition for a Mermin scenario provides a crisp operational interpretation for strong complementarity. We also provide a complete classification of strongly complementary observables for quantum theory, something which has not yet been achieved for ordinary complementarity.  Since our main results are expressed in a diagrammatic language (the one of dagger-compact categories) they can be applied outside of quantum theory, in any setting which supports the purely algebraic notion of strongly complementary observables. We have therefore introduced a method for discussing non-locality in a wide variety of models in addition to quantum theory.    The diagrammatic calculus substantially simplifies (and sometimes even trivialises) many of the derivations, and provides new insights. In particular, the diagrammatic computation of correlations clearly shows how local measurements interact to yield a global overall effect. In other words, we depict non-locality.   This is joint work with Ross Duncan, Aleks Kissinger and Quanlong (Harny) Wang. Paper: arXiv:1203.4988 - LiCS'12