Article
Sampling quantum nonlocal correlations with high probability
Author/s | González Guillén, Carlos Eduardo
Jiménez Gómez, Carlos Hugo Palazuelos Cabezón, Carlos Villanueva Díez, Ignacio |
Department | Universidad de Sevilla. Departamento de Análisis Matemático |
Publication Date | 2016-05 |
Deposit Date | 2016-10-03 |
Published in |
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Abstract | It is well known that quantum correlations for bipartite dichotomic measurements are those of the form γ=(⟨ui,vj⟩)ni,j=1, where the vectors ui and vj are in the unit ball of a real Hilbert space. In this work we study the ... It is well known that quantum correlations for bipartite dichotomic measurements are those of the form γ=(⟨ui,vj⟩)ni,j=1, where the vectors ui and vj are in the unit ball of a real Hilbert space. In this work we study the probability of the nonlocal nature of these correlations as a function of α=mnα=mn, where the previous vectors are sampled according to the Haar measure in the unit sphere of RmRm. In particular, we prove the existence of an α0>0 such that if α≤α0, γ is nonlocal with probability tending to 1 as n→∞, while for α>2, γ is local with probability tending to 1 as n→∞. |
Funding agencies | Ministerio de Economía y Competitividad (MINECO). España Consejo Nacional de Ciencia y Tecnología (CONACYT). México |
Project ID. | info:eu-repo/grantAgreement/MINECO/MTM2011-26912
info:eu-repo/grantAgreement/MINECO/MTM2012-30748 180486 |
Citation | González Guillén, C.E., Jiménez Gómez, C.H., Palazuelos Cabezón, C. y Villanueva Díez, I. (2016). Sampling quantum nonlocal correlations with high probability. Communications in Mathematical Physics, 344 (1), 141-154. |
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