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arXiv:quant-ph/0409051 · Physics Letters A

Violation of a Bell inequality in particle physics experimentally verified?

Reinhold A. Bertlmann, A. Bramòn, Gianni Garbarino, Beatrix C. Hiesmayr

Published Oct 21, 2004• 51 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2004.10.006

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It is often believed that de Finetti's coherence principle naturally leads, in the finite case, to the Kolmogorov's probability theory of random phenomena, which then implies Bell's inequality.Thus, not only a violation of Bell's inequality looks paradoxical in the Kolmogorovian framework, but it should violate also de Finetti's coherence principle.Firstly, we show that this is not the case: the typical theoretical violations of Bell's inequality in quantum physics are in agreement with de Finetti's coherence principle.Secondly, we look for statistical evidence of such violations: we consider the experimental data of measurements of polarization of photons, performed to verify empirically violations of Bell's inequality, and, on the basis of the estimated violation, we test the null hypothesis of Kolmogorovianity for the observed phenomenon.By standard inferential techniques we compute the pvalue for the test and get a clear strong conclusion against the Kolmogorovian hypothesis.
We report the experimental violation of Leggett-type inequalities for a hybrid entangled state of spin and orbital angular momentum of a single photon. These inequalities give a physical criterion to verify the possible validity of a class of hidden-variable theories, originally named ``crypto nonlocal,'' that are not excluded by the violation of Bell-type inequalities. In our case, the tested theories assume the existence of hidden variables associated with independent degrees of freedom of the same particle, while admitting the possibility of an influence between the two measurements, i.e., the so-called contextuality of observables. We observe a violation of the Leggett inequalities for a range of experimental inputs, with a maximum violation of seven standard deviations, thus ruling out this class of hidden-variable models with a high level of confidence.
It is possible for two parties, Alice and Bob, to establish a secure communication link by sharing an ensemble of entangled particles, and then using these particles to generate a secret key. One way to establish that the particles are indeed entangled is to verify that they violate a Bell inequality. However, it might be the case that Bob is not trustworthy and wishes Alice to believe that their communications are secure, when in fact they are not. He can do this by managing to have prior knowledge of Alice's measurement device settings and then modifying his own settings based upon this information. In this case it is possible for shared particle states that must satisfy a Bell inequality to appear to violate this inequality, which would also make the system appear secure. When Bob modifies his measurement settings, however, he produces false correlations. Here we demonstrate experimentally that Alice can detect these false correlations, and uncover Bob's trickery, by using loop-state-preparation-and-measurement (SPAM) tomography. More generally, we demonstrate that loop SPAM tomography can detect false correlations (correlated errors) in a two-qubit system without needing to know anything about the prepared states or the measurements, other than the dimensions of the operators that describe them.