Experimental Test of Bell's Inequalities Using Time- Varying Analyzers

Abstract

for trapping as 6 decreases is reflective of the incorporation of periodic components into the sequence of numbers generated.To summarize the motivation and principal conclusion of this Letter, we restate' that for values of b where numerically generated sequences~P Pear to be chaotic, it has not been settled whether those sequences "are truly chaotic, or whether, in fact, they are really periodic, but with exceedingly large periods and very long transients required to settle down. " On the one hand, Grossman and Thomae" have suggested that (only) the parameter value b =1 generates pure chaos [see the discussion following Eq. (31) of Ref. 5 and the correlations plotted in their Fig. 9]. On the other hand, for certa, in other values of b, numberical results of Lorenz (reported in Ref. 1) "strongly suggest that the sequences are truly chaotic. " The purpose of this communication was to use an independent and exact result from the statistical-mechanical theory of d =1 random walks to test the randomness of the parabolic map for parameter values where the existence of "true chaos" is still an open question.Our results strongly support the conclusions of Grossmann and Thomae.Correlations of linear polarizations of pairs of photons have been measured with time-varying analyzers. The analyzer in each leg of the apparatus is an acousto-optical switch followed by two linear polarizers. The switches operate at incommensurate frequencies near 50 MHz. Each analyzer amounts to a polarizer which jumps between two orientations in a time short compared with the photon transit time. The results are in good agreement with quantum mechanical predictions but violate Bell's inequalities by 5 standard deviations.

The ultimate physical limits of privacy

“…Shocking as it may be, our world is not of this kind. Statistical inequalities, such as e = 1/4, derived on the assumption that the values of unmeasured physical quantities do exist and commonly referred to as Bell's inequalities 33 , have been violated in a number of painstaking experiments 33,34,35,36,37,38,39,40,41,42,43,44 . We shall not dwell on the philosophical implications of this experimental fact (volumes have been written on the subject), but simply point out that it should be embraced by all those who worry about secrecy because what does not exist cannot be eavesdropped, and so it is much easier to keep secrets in a non-classical world.…”

Bell violation using entangled photons without the fair-sampling assumption

“…The two other main assumptions include "locality" (10,11) and "freedom of choice" (12). Invoking any of these renders an experiment vulnerable to explanation by a local realistic theory.…”

Bell Inequality and Its Application to Cosmology

“…Thus, the maximal violation of Bell inequality in quantum mechanics has the extra √ 2 factor in the case of a pair of spins [16]. This violation was convincingly tested by Aspect et al [2,3] (see Figure 1) and the quantum entanglement was confirmed as a fundamental aspect of quantum mechanics. 1 To avoid confusion, the tensor product ⊗ is omitted below for simplicity.…”

“…After Aspect et al succeeded in showing experimental evidence of the quantum nature of entanglement by measuring correlations of linear polarizations of pairs of photons [2,3], much attention has been paid to this genuine quantum property in various research areas in quantum information theory.…”