Strong complementarity and non-locality in categorical quantum mechanics
Coecke, Bob and Duncan, Ross and Kissinger, Aleks and Wang, Quanlong; (2012) Strong complementarity and non-locality in categorical quantum mechanics. In: Logic in Computer Science (LICS), 2012 27th Annual IEEE Symposium on. IEEE, HRV, pp. 245-254. ISBN 9781467322638 (https://doi.org/10.1109/LICS.2012.35)
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Categorical quantum mechanics studies quantum theory in the framework of dagger-compact closed categories. Using this framework, 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 the (diagrammatic) language 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.
ORCID iDs
Coecke, Bob, Duncan, Ross ORCID: https://orcid.org/0000-0001-6758-1573, Kissinger, Aleks and Wang, Quanlong;-
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Item type: Book Section ID code: 45794 Dates: DateEvent2012PublishedNotes: Proceedings of the 27th Annual IEEE Symposium on Logic in Computer Science. (LiCS2012) pp 245--254 IEEE Computer Society Press Subjects: Science > Mathematics > Electronic computers. Computer science
Science > PhysicsDepartment: Faculty of Science > Computer and Information Sciences Depositing user: Pure Administrator Date deposited: 11 Nov 2013 10:35 Last modified: 01 Sep 2024 02:39 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/45794