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Abstract
We study the classical and quantum values of a class of one-and two-party unique games, that generalizes the well-known XOR games to the case of non-binary outcomes. In the bipartite case the generalized XOR(XOR-d) games we study are a subclass of the well-known linear games. We introduce a 'constraint graph' associated to such a game, with the constraints defining the game represented by an edge-coloring of the graph. We use the graph-theoretic characterization to relate the task of finding equivalent games to the notion of signed graphs and switching equivalence from graph theory. We relate the problem of computing the classical value of single-party anti-correlation XOR games to finding the edge bipartization number of a graph, which is known to be MaxSNP hard, and connect the computation of the classical value of XOR-d games to the identification of specific cycles in the graph. We construct an orthogonality graph of the game from the constraint graph and study its Lovasz theta number as a general upper bound on the quantum value even in the case of single-party contextual XOR-d games. XOR-d games possess appealing properties for use in device-independent applications such as randomness of the local correlated outcomes in the optimal quantum strategy. We study the possibility of obtaining quantum algebraic violation of these games, and show that no finite XOR-d game possesses the property of pseudo-telepathy leaving the frequently used chained Bell inequalities as the natural candidates for such applications. We also show this lack of pseudo-telepathy for multi-party XOR-type inequalities involving two-body correlation functions.
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Authors (7)
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Ravishankar Ramanathan
- Uniwersytet Gdański Krajowe Centrum Informatyki Kwantowej
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Piotr Gnaciński
- Uniwersytet Gdański Krajowe Centrum Informatyki Kwantowej
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Karol Horodecki
- Uniwersytet Gdański Wydzaił Matematyki, Fizyki i Informatyki
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Michał Horodecki
- Uniwersytet Gdański Krajowe Centrum Informatyki Kwantowej
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S Severini
- University College Department of Computer Science and Department of Physics and Astronomy
Cite as
Full text
- Publication version
- Accepted or Published Version
- DOI:
- Digital Object Identifier (open in new tab) 10.1088/1367-2630/18/4/045020
- License
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Details
- Category:
- Articles
- Type:
- artykuł w czasopiśmie wyróżnionym w JCR
- Published in:
-
NEW JOURNAL OF PHYSICS
no. 18,
pages 1 - 23,
ISSN: 1367-2630 - Language:
- English
- Publication year:
- 2016
- Bibliographic description:
- Rosicka M., Ramanathan R., Gnaciński P., Horodecki K., Horodecki M., Horodecki P., Severini S.: Linear game non-contextuality and Bell inequalities—a graph-theoretic approach// NEW JOURNAL OF PHYSICS. -Vol. 18, (2016), s.1-23
- DOI:
- Digital Object Identifier (open in new tab) 10.1088/1367-2630/18/4/045020
- Verified by:
- Gdańsk University of Technology
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