Gustavo Cañas, Johanna F. Barra, Esteban S. Gómez, Gustavo Lima, Fabio Sciarrino, Adan Cabello
Loophole-free Bell tests for quantum nonlocality and long-distance secure communication require photo-detection efficiencies beyond a threshold eta which depends on the Bell inequality and the noise affecting the state received by the distant parties. Most calculations of eta assume that the noise is random and can be modeled as white noise. However, in a recent proposal for a loophole-free Bell test [A. Cabello and F. Sciarrino, Phys. Rev. X 2, 021010 (2012)], a specific colored noise appears as a consequence of the precertification of the photon's presence through single photon spontaneous parametric down-conversion. Here we obtain eta and the optimal quantum states and local settings for the precertification scheme, as a function of the amount of colored noise for three bipartite Bell inequalities with n dichotomic settings: CHSH (n=2), I3322 (n=3), and A5 (n=4), both for the case of symmetric efficiencies, corresponding to photon-photon Bell tests, and for the totally asymmetric case, corresponding to atom-photon Bell tests. Remarkably, in all these cases, eta is robust against the colored noise and smaller than the eta needed when a similar level of white noise affects the state. More importantly, the conditions required for a loophole-free experiment are fulfilled for realistic photo-detection efficiencies. The present analysis can find application in any physical system adopted to carry out Bell inequalities in which the dominant noise is a colored one.
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http://arxiv.org/abs/1206.2290
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