Stefano Gogioso ; William Zeng - Generalised Mermin-type non-locality arguments

lmcs:3284 - Logical Methods in Computer Science, April 26, 2019, Volume 15, Issue 2 - https://doi.org/10.23638/LMCS-15(2:3)2019
Generalised Mermin-type non-locality arguments

Authors: Stefano Gogioso ; William Zeng

We broadly generalise Mermin-type arguments on GHZ states, and we provide exact group-theoretic conditions for non-locality to be achieved. Our results are of interest in quantum foundations, where they yield a new hierarchy of quantum-realisable All-vs-Nothing arguments. They are also of interest to quantum protocols, where they find immediate application to a non-trivial extension of the hybrid quantum-classical secret sharing scheme of Hillery, Bu\v{z}ek and Berthiaume (HBB). Our proofs are carried out in the graphical language of string diagrams for dagger compact categories, and their validity extends beyond quantum theory to any theory featuring the relevant algebraic structures.


Volume: Volume 15, Issue 2
Published on: April 26, 2019
Accepted on: April 26, 2019
Submitted on: April 25, 2017
Keywords: Quantum Physics,Computer Science - Logic in Computer Science,Mathematics - Category Theory,F.1.1,F.3.2


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