RT Journal Article
T1 Random Quantum Correlations are Generically Non-classical
A1 González-Guillén, Carlos E.
A1 Lancien, Cécilia
A1 Palazuelos Cabezón, Carlos
A1 Villanueva Díez, Ignacio
AB It is now a well-known fact that the correlations arising from local dichotomic measurements on an entangled quantum state may exhibit intrinsically non-classical features. In this paper we delve into a comprehensive study of random instances of such bipartite correlations. The main question we are interested in is: given a quantum correlation, taken at random, how likely is it that it is truly non-explainable by a classical model? We show that, under very general assumptions on the considered distribution, a random correlation which lies on the border of the quantum set is with high probability outside the classical set. What is more, we are able to provide the Bell inequality certifying this fact. On the technical side, our results follow from (i) estimating precisely the “quantum norm” of a random matrix and (ii) lower-bounding sharply enough its “classical norm”, hence proving a gap between the two. Along the way, we need a non-trivial upper bound on the   ∞→1∞→1  norm of a random orthogonal matrix, which might be of independent interest.
PB Springer
SN 1424-0637
YR 2017
FD 2017
LK https://hdl.handle.net/20.500.14352/18275
UL https://hdl.handle.net/20.500.14352/18275
LA eng
NO González Guillén, C. E., Lancien, C., Palazuelos Cabezón, C. et al. «Random Quantum Correlations Are Generically Non-Classical». Annales Henri Poincaré, vol. 18, n.o 12, diciembre de 2017, pp. 3793-813. DOI.org (Crossref), https://doi.org/10.1007/s00023-017-0615-9.
NO Unión Europea
NO Ministerio de Economía, Comercio y Empresa (España)
NO Comunidad de Madrid
NO Generalitat de Catalunya
NO French CNRS (ANR)
DS Docta Complutense
RD 10 abr 2025