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Experimental tests of Bell's inequality allow to distinguish quantum mechanics from local hidden variable theories.
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For entanglement swapping this is a conservative assumption, since there the noise might be entangled (see A. Sen et al., Phys. Rev. A 68, 062301 (2003)
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Other proposals for loophole-free tests of Bell inequalities are described in P. H. Eberhard et al., Phys. Rev A 47, R747 (1993)
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It can be shown that the spatial mode filtering given by the single-mode optical fiber leads to observation of a maximally entangled state for an arbitrarily large numerical aperture of the photon collecting optics
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