We consider quantum XOR games, defined in the work of Regev and Vidick [ACM Trans. Comput. Theory 7, 43 (2015)], from the perspective of unitary correlations defined in the work of Harris and Paulsen [Integr. Equations Oper. Theory 89, 125 (2017)]. We show that the winning bias of a quantum XOR game in the tensor product model (respectively, the commuting model) is equal to the norm of its associated linear functional on the unitary correlation set from the appropriate model. We show that Connes’ embedding problem has a positive answer if and only if every quantum XOR game has entanglement bias equal to the commuting bias. In particular, the embedding problem is equivalent to determining whether every quantum XOR game G with a winning strategy in the commuting model also has a winning strategy in the approximate finite-dimensional model.
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December 2017
Research Article|
December 20 2017
Connes’ embedding problem and winning strategies for quantum XOR games
Samuel J. Harris
Samuel J. Harris
a)
University of Waterloo
, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada
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Electronic mail: [email protected]
J. Math. Phys. 58, 122203 (2017)
Article history
Received:
August 28 2017
Accepted:
December 04 2017
Citation
Samuel J. Harris; Connes’ embedding problem and winning strategies for quantum XOR games. J. Math. Phys. 1 December 2017; 58 (12): 122203. https://doi.org/10.1063/1.5001930
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