The quantum-to-classical graph homomorphism game
| Autor: | Michael Brannan, Priyanga Ganesan, Samuel J. Harris |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Computer Science::Computer Science and Game Theory
Quantum Physics ComputerSystemsOrganization_MISCELLANEOUS FOS: Mathematics ComputingMilieux_PERSONALCOMPUTING Mathematics - Operator Algebras FOS: Physical sciences Statistical and Nonlinear Physics Operator Algebras (math.OA) Quantum Physics (quant-ph) Mathematical Physics |
| Popis: | Motivated by non-local games and quantum coloring problems, we introduce a graph homomorphism game between quantum graphs and classical graphs. This game is naturally cast as a "quantum-classical game"--that is, a non-local game of two players involving quantum questions and classical answers. This game generalizes the graph homomorphism game between classical graphs. We show that winning strategies in the various quantum models for the game is an analogue of the notion of non-commutative graph homomorphisms due to D. Stahlke [44]. Moreover, we present a game algebra in this context that generalizes the game algebra for graph homomorphisms given by J.W. Helton, K. Meyer, V.I. Paulsen and M. Satriano [22]. We also demonstrate explicit quantum colorings of all quantum complete graphs, yielding the surprising fact that the algebra of the $4$-coloring game for a quantum graph is always non-trivial, extending a result of [22]. v2: fixed errors in proofs of the old Theorem 4.7 and 5.6; removed Lemma 4.8 |
| Databáze: | OpenAIRE |
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