Perfect Commuting-Operator Strategies for Linear System Games
Abstract
Linear system games are a generalization of Mermin's magic square game introduced by Cleve and Mittal. They show that perfect strategies for linear system games in the tensor-product model of entanglement correspond to finite-dimensional operator solutions of a certain set of non-commutative equations. We investigate linear system games in the commuting-operator model of entanglement, where Alice and Bob's measurement operators act on a joint Hilbert space, and Alice's operators must commute with Bob's operators. We show that perfect strategies in this model correspond to possibly-infinite-dimensional operator solutions of the non-commutative equations. The proof is based around a finitely-presented group associated to the linear system which arises from the non-commutative equations.
Keywords
Cite
@article{arxiv.1606.02278,
title = {Perfect Commuting-Operator Strategies for Linear System Games},
author = {Richard Cleve and Li Liu and William Slofstra},
journal= {arXiv preprint arXiv:1606.02278},
year = {2017}
}