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Sampling quantum nonlocal correlations with high probability

 

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Author: González Guillén, Carlos Eduardo
Jiménez Gómez, Carlos Hugo
Palazuelos Cabezón, Carlos
Villanueva Díez, Ignacio
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 2016-05
Published in: Communications in Mathematical Physics, 344 (1), 141-154.
Document type: Article
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 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→∞.
Cite: 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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URI: http://hdl.handle.net/11441/46742

DOI: 10.1007/s00220-016-2625-8

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