Unbounded violations of bipartite Bell Inequalities via Operator Space theory
| dc.contributor.author | Junge, Marius | |
| dc.contributor.author | Palazuelos Cabezón, Carlos | |
| dc.contributor.author | Pérez García, David | |
| dc.contributor.author | Villanueva Díez, Ignacio | |
| dc.contributor.author | Wolf, Michael M. | |
| dc.date.accessioned | 2023-06-20T00:02:17Z | |
| dc.date.available | 2023-06-20T00:02:17Z | |
| dc.date.issued | 2010-12 | |
| dc.description.abstract | In this work we show that bipartite quantum states with local Hilbert space dimension n can violate a Bell inequality by a factor of order Ω(√n∕Log2n) when observables with n possible outcomes are used. A central tool in the analysis is a close relation between this problem and operator space theory and, in particular, the very recent noncommutative Lp embedding theory. As a consequence of this result, we obtain better Hilbert space dimension witnesses and quantum violations of Bell inequalities with better resistance to noise. | en |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Unión Europea - FP7 | |
| dc.description.sponsorship | Comunidad de Madrid | |
| dc.description.sponsorship | National Science Foundation (Estados Unidos) | |
| dc.description.sponsorship | Danish Center for Quantum Optics | |
| dc.description.sponsorship | Danish Natural Science Research Council | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/10961 | |
| dc.identifier.citation | Junge, M., Palazuelos Cabezón, C., Pérez García, D., Villanueva Díez, I., Wolf, M. M. «Unbounded Violations of Bipartite Bell Inequalities via Operator Space Theory». Communications in Mathematical Physics, vol. 300, n.o 3, diciembre de 2010, pp. 715-39. DOI.org (Crossref), https://doi.org/10.1007/s00220-010-1125-5. | |
| dc.identifier.doi | 10.1007/s00220-010-1125-5 | |
| dc.identifier.issn | 0010-3616 | |
| dc.identifier.officialurl | https//doi.org/10.1007/s00220-010-1125-5 | |
| dc.identifier.relatedurl | http://link.springer.com/article/10.1007/s00220-010-1125-5 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/41777 | |
| dc.issue.number | 3 | |
| dc.journal.title | Communications in Mathematical Physics | |
| dc.language.iso | eng | |
| dc.page.final | 739 | |
| dc.page.initial | 715 | |
| dc.publisher | Springer | |
| dc.relation.projectID | QUEVADIS (233859) | |
| dc.relation.projectID | QUITEMAD-CM (S2009/ESP-1594) | |
| dc.relation.projectID | (DMS-0901457) | |
| dc.relation.projectID | I-MATH | |
| dc.relation.projectID | (MTM2008-01366) | |
| dc.relation.projectID | QUANTOP | |
| dc.relation.projectID | COQUIT | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.982.22 | |
| dc.subject.keyword | Banach-spaces | |
| dc.subject.keyword | Quantum entanglement | |
| dc.subject.keyword | Quantum Physics | |
| dc.subject.ucm | Análisis matemático | |
| dc.subject.ucm | Teoría de los quanta | |
| dc.subject.ucm | Física matemática | |
| dc.subject.ucm | Teoría cuántica | |
| dc.subject.unesco | 1202 Análisis y Análisis Funcional | |
| dc.subject.unesco | 2210.23 Teoría Cuántica | |
| dc.title | Unbounded violations of bipartite Bell Inequalities via Operator Space theory | en |
| dc.type | journal article | |
| dc.volume.number | 300 | |
| dcterms.references | Acin, A., Brunner, N., Gisin, N., Massar, S., Pironio, S., Scarani, V.: Device-independent security of quantum cryptography against collective attacks. Phys. Rev. Lett. 98, 230501 (2007) Acin, A., Masanes, L., Gisin, N.: From Bell's Theorem to Secure Quantum Key Distribution. Phys. Rev. Lett. 97, 120405 (2006) Bell, J.S.: On the Einstein-Poldolsky-Rosen paradox. Physics 1, 195 (1964) Bennett, C., Sharpley, R.: Interpolation of operators. London-New York: Academic Press, 1988 Ben-Or, M., Hassidim, A., Pilpel, H.: Quantum Multi Prover Interactive Proofs with Communicating Provers. In: Proceedings of 49th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2008), Los Alamitos, CA: IEEE, 2008 Brassard, G., Broadbent, A., Tapp, A.: Quantum Pseudo-Telepathy. Found. Phys. 35(11), 1877–1907 (2005) Briët, J., Buhrman, H., Toner, B.: A generalized Grothendieck inequality and entanglement in XOR games. http://arXiv.org/abs/0901.2009v1 [quant-ph], 2009 Brunner, N., Gisin, N., Scarani, V., Simon, C.: Detection loophole in asymmetric Bell experiments. Phys. Rev. Lett. 98, 220403 (2007) Brunner, N., Pironio, S., Acin, A., Gisin, N., Methot, A.A., Scarani, V.: Testing the Hilbert space dimension. Phys. Rev. Lett. 100, 210503 (2008) Buhrman, H., Cleve, R., Massar, S., de Wolf, R.: Non-locality and Communication Complexity. Rev. Mod. Phys. 82, 665 (2010) Cabello, A., Larsson, J.-A.: Minimum detection efficiency for a loophole-free atom-photon Bell experiment. Phys. Rev. Lett. 98, 220402 (2007) Cabello, A., Rodriguez, D., Villanueva, I.: Necessary and sufficient detection efficiency for the Mermin inequalities. Rev. Lett. 101, 120402 (2008) Cleve, R., Høyer, P., Toner, B., Watrous, J.: Consequences and Limits of Nonlocal Strategies. In: Proceedings of the 19th IEEE Annual Conference on Computational Complexity (CCC 2004), Los Alamitos, CA: IEEE, pp. 236–249. Cleve, R., Gavinsly, D., Jain, R.: Entanglement-Resistant Two-Prover Interactive Proof Systems and Non-Adaptive Private Information Retrieval Systems. http://arXiv.org/abs/quant-ph/0707.1729v1 [quant-ph], 2007 Cohen, A., Dahmen, W., DeVore, R.: Compressed sensing and best k-term approximation. JAMS 22(1), 211–231 (2009) Collins, D., Gisin, N.: A relevant two qubit Bell inequality inequivalent to the CHSH inequality. J. Phys. A: Math. Gen. 37, 1775–1787 (2004) Defant, A., Floret, K.: Tensor Norms and Operator Ideals. Amsterdam: North-Holland, 1993 Degorre, J., Kaplan, M., Laplante, S., Roland, J.: The communication complexity of non-signaling distributions. Lect. Notes Comp. Sci. 5734, 270–281 (2009) Doherty, A.C., Liang, Y-C., Toner, B., Wehner, S.: The quantum moment problem and bounds on entangled multi-prover games. In: Proc. of IEEE Conference on Computational Complexity 2008, Los Alamitos, CA: IEEE, pp. 199–210 MR2513501 (2010e:81058) Effros, E.G., Ruan, Z.-J.: Operator spaces. London Math. Soc. Monographs New Series, Oxford: Clarendon Press, 2000 MR1793753 (2002a:46082) Einstein, A., Podolsky, B., Rosen, N.: Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Phys. Rev. 47, 777 (1935) Grothendieck, A.: Résumé de la théorie métrique des produits tensoriels topologiques (French). Bol. Soc. Mat. S~ao Paulo 8, 1–79 (1953) Holenstein, T.: Parallel repetition: simplifications and the no-signaling case. In: Proceedings of the thirty-ninth annual ACM symposium on Theory of computing STOC 2007, New York: Assoc. for Computing Machinery, 2007 Jain, R., Ji, Z., Upadhyay, S., Watrous, J.: QIP = PSPACE. http://arXiv.org./abs/0907.4737v2 [quant-ph], 2009 Junge, M.: Factorization theory for Spaces of Operators. Habilitationsschrift Kiel, 1996; see also: http://www.math.uiuc.edu/∼mjunge/publish.html Junge, M., Parcet, J.: Rosenthal's theorem for subspaces of noncommutative Lp. Duke Math. J. 141, 75–122 (2008) Junge, M., Parcet, J.: Mixed-norm inequalities and operator space Lp embedding theory. Mem. Amer. Math. Soc. 952 (2010) Junge, M., Parcet, J.: A transference method in quantum probability. Adv. Math. 225, 389–444 (2010) Junge, M., Parcet, J., Xu, Q.: Rosenthal type inequalities for free chaos. Ann. Probab. 35, 1374–1437 (2007) Kempe, J., Regev, O., Toner, B.: The Unique Games Conjecture with Entangled Provers is False. In: Proceedings of 49th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2008), Los Alamitos, CA: IEEE, 2008 Kempe, J., Kobayashi, H., Matsumoto, K., Toner, B., Vidick, T.: Entangled games are hard to approximate. http://arXiv.org/abs/0704.2903v2 [quant-ph], 2007 Khot, S., Vishnoi, N.K.: The unique games conjecture, integrality gap for cut problems and embeddability of negative type metrics into ℓ1. In: Proc. 46th IEEE Symp. on Foundations of Computer Science, Los Alamitos, CA: IEEE, 2005, pp. 53–62 Kraus B. Gisin N.Renner, R.: Lower and upper bounds on the secret key rate for QKD protocols using one-way classical communication. Phys. Rev. Lett. 95, 080501 (2005) Ledoux, M., Talagrand, M.: Probability in Banach Spaces. Berlin-Heidelberg-New York: Springer-Verlag, 1991 Marcus, M.B., Pisier, G.: Random Fourier series with applications to Harmonic Analysis. Annals of Math. Studies, 101, Princeton, NJ: Princeton Univ. Press, 1981 Masanes, Ll., Renner, R., Winter, A., Barrett, J., Christandl, M.: Security of key distribution from causality constraints. http://arXiv.org/abs/quant-ph/0606049v4 (2006) Masanes, L.: Universally-composable privacy amplification from causality constraints. Phys. Rev. Lett. 102, 140501 (2009) Massar, S.: Nonlocality, closing the detection loophole, and communication complexity. Phys. Rev. A 65, 032121 (2002) Massar, S., Pironio. S.: Violation of local realism vs detection efficiency. Phys. Rev. A 68, 062109 (2003) Paulsen, V.I.: Completely Bounded Maps and Operator Algebras. Cambridge Studies in Advanced Mathematics 78, Cambridge: Cambridge University Press, 2003 Pearle, P.M.: Hidden-variable example based upon data rejection. Phys. Rev. D 2, 1418 (1970) Pérez-García, D., Wolf, M.M., Palazuelos, C., Villanueva, I., Junge, M.: Unbounded violation of tripartite Bell inequalities. Commun. Math. Phys. 279(2), 455–486 (2008) Pisier, G.: An Introduction to Operator Spaces. London Math. Soc. Lecture Notes Series 294, Cambridge: Cambridge University Press, 2003 Pisier, G.: The volume of convex bodies and Banach Space Geometry. Cambridge: Cambridge University Press, 1989 Pisier, G.: Factorization of linear operators and geometry of Banach spaces. CBMS 60, Providence, RI: Amer. Math. Soc., 1986 Pitowsky, I.: New Bell inequalities for the singlet state: Going beyond the Grothendieck bound. J. Math. Phys. 49, 012101 (2008) Rao, A.: Parallel repetition in projection games and a concentration bound. In: 40th STOC Proc, STOC2008, New York: Assoc. for Computing Machinery, 2008 Raz, R.: A Parallel Repetition Theorem. SIAM J. Comp. 27, 763–803 (1998) Shor, P.W., Preskill, J.: Simple Proof of Security of the BB84 Quantum Key Distribution Protocol. Phys. Rev. Lett. 85, 441–444 (2000) Tomczak-Jaegermann, N.: Banach-Mazur Distances and Finite Dimensional Operator Ideals. Pitman Monographs and Surveys in Pure and Applied Mathematics 38, London: Longman Scientific and Technical, 1989 Tsirelson, B.S.: Hadronic Journal Supplement 84, 329–345 (1993) Vertesi, T., Pal, K.F.: Bounding the dimension of bipartite quantum systems. Phys. Rev. A 79, 042106 (2009) Wehner, S., Christandl, M., Doherty, A.C.: A lower bound on the dimension of a quantum system given measured data. Phys. Rev. A 78, 062112 (2008) Werner, R.F., Wolf, M.M.: Bell inequalities and Entanglement. Quant. Inf. Comp. 1(3), 1–25 (2001) Wolf, M.M., Pérez-García, D.: Assessing dimensions from evolution. Phys. Rev. Lett. 102, 190504 (2009) | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 09970d9e-6722-4f02-aac0-023cf9867638 | |
| relation.isAuthorOfPublication | 5edb2da8-669b-42d1-867d-8fe3144eb216 | |
| relation.isAuthorOfPublication | 45785a65-66ff-415c-a422-bfdc6e3ff149 | |
| relation.isAuthorOfPublication.latestForDiscovery | 5edb2da8-669b-42d1-867d-8fe3144eb216 |
