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Quantum one-way versus classical two-way communication in XOR games

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dc.contributor.authorAmr, Abderramán
dc.contributor.authorVillanueva, Ignacio
dc.date.accessioned2023-06-17T09:03:53Z
dc.date.available2023-06-17T09:03:53Z
dc.date.issued2021
dc.description.abstractIn this work, we give an example of exponential separation between quantum and classical resources in the setting of XOR games assisted with communication. Specifically, we show an example of a XOR game for which O(n) bits of two-way classical communication are needed in order to achieve the same value as can be attained with logn qubits of one-way communication. We also find a characterization for the value of a XOR game assisted with a limited amount of two-way communication in terms of tensor norms of normed spaces.
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedFALSE
dc.description.sponsorshipMinisterio de Economía y Competitividad (MINECO)
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/65185
dc.identifier.citation1. Brunner, N., Cavalcanti, D., Pironio, S., Scarani, V., Wehner, S.: Bell nonlocality. Rev. Mod. Phys. 86, 419 (2014) 2. Bell, J.S.: On the Einstein–Podolsky–Rosen paradox. Physics 1, 195 (1964) 3. Tsirelson, B.S.: Some results and problems on quantum Bell-type inequalities. Hadron. J. Suppl. 8(4), 329–345 (1993) 4. Pérez-García, D., Wolf, M.M., Palazuelos, C., Villanueva, I., Junge, M.: Unbounded violation of tripartite Bell inequalities. Commun. Math. Phys. 279, 455–486 (2008) 5. Briet, J., Vidick, T.: Explicit lower and upper bounds on the entangled value of multiplayer XOR games. Commun. Math. Phys. 321, 181–207 (2013) 6. Palazuelos, C., Vidick, T.: Survey on nonlocal games and operator space theory. J. Math. Phys. 57, 015220 (2016) 7. Kushilevitz, E., Nisan, N.: Communication Complexity. Cambridge University Press, Cambridge (2006) 8. Yao, A.C.: Quantum circuit complexity. In: Proceedings 34th Annual Symposium on Foundations of Computer Science, FOCS 93, pp. 352–361 (1993) 9. Cleve, R., Buhrman, H.: Substituting quantum entanglement for communication. Phys. Rev. A 56, 1201–1204 (1997) 10. Bennett, C.H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70, 1895–1899 (1993) 11. Regev, O., Klartag, B.: Quantum one-way communication can be exponentially stronger than classical communication. In: Proceedings of the 43rd Annual ACM Symposium on Theory of Computing, pp. 31–40. ACM, San Jose, CA, USA (2011) 12. Raz, R.: Exponential separation of quantum and classical communication complexity. In: Proceedings of the 31st Annual ACM Symposium on the Theory of Computing, pp. 358–367 (1999) 13. Buhrman, H., Czekaj, L., Grudka, A., Horodecki, M., Horodecki, P., Markiewicz, M., Speelman, F., Strelchuk, S.: Quantum communication complexity advantage implies violation of a Bell inequality. PNAS 113(12), 3191–3196 (2016) 14. Junge, M., Palazuelos, C., Villanueva, I.: Classical vs. quantum communication in XOR games. Quantum Inf. Proc. 17, 117 (2018) 15. Defant, A., Floret, K.: Tensor Norms and Operator Ideals. North-Holland, Amsterdam (1993) 16. Ryan, R.A.: Introduction to Tensor Products of Banach Spaces. ISBN 978-1-4471-3903-4 (2002)
dc.identifier.doi10.1007/s11128-021-03014-2
dc.identifier.issn1570-0755
dc.identifier.officialurlhttps://doi.org/10.1007/s11128-021-03014-2
dc.identifier.relatedurlhttps://link.springer.com/article/10.1007/s11128-021-03014-2
dc.identifier.urihttps://hdl.handle.net/20.500.14352/8077
dc.journal.titleQuantum Information Processing
dc.language.isoeng
dc.publisherSpringer
dc.relation.projectIDMTM2017-88385-P; MTM2014-54240-P
dc.rights.accessRightsopen access
dc.subject.cdu517.98
dc.subject.keywordXOR games
dc.subject.keywordCommunication complexity
dc.subject.keywordTensor norms
dc.subject.ucmAnálisis funcional y teoría de operadores
dc.titleQuantum one-way versus classical two-way communication in XOR games
dc.typejournal article
dc.volume.number20
dspace.entity.typePublication
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