A non-dichotomic Bell-type inequality for macroscopic photon numbers in two spatially separated beams is derived from local realistic assumptions. This inequality is shown to be possible to violate with the macroscopic Bell states recently obtained in experiment.
We present a novel Bell inequality that does not require dichotomic (two-outcome) measurements. It is based on an inequality originally derived by Wigner in 1969, extending it such that no assumptions other than local-realism, fair-sampling, and freedom-of-choice are necessary. It is most useful in situations where there is no direct access to true two-outcome (dichotomic) measurements, like photonic quantum experiments where spatial degrees-of-freedoms are often analyzed with spatial light modulators (SLMs), as well as many other experimental scenarios. The only other class of inequalities (CH-type) that has this feature requires coincidence and single count-rates to be of the same order of magnitude for violation, ours does not. It thereby enables the stringent verification of entanglement and rejection of local-realism, without any assumptions about the underlying Hilbert-space, such as dimensionality – in the most dificult experimental conditions. We also experimentally violate this inequality in a novel setup: entangled states of very high orbital angular momentum. This constitutes a rejection of the hypothesis of local realism (under reasonable assumptions) with the highest quanta to date.
We suggest a method to test the premise of ``macroscopic local realism'' that is sufficient to derive Bell inequalities when measurements of photon numbers are only accurate to an uncertainty of order n photons, where n is macroscopic. Macroscopic local realism is only sufficient to imply, in the context of the original Einstein-Podolsky-Rosen argument, fuzzy ``elements of reality'' that have a macroscopic indeterminacy. We show therefore how the violation of local realism in the presence of macroscopic uncertainties implies the failure of macroscopic local realism. Quantum states violating this macroscopic local realism are presented.
In the experimental verification of Bell’s inequalities in real photonic experiments, it is generally believed that the so-called fair sampling assumption (which means that a small fraction of results provide a fair statistical sample) has an unavoidable role. Here, we want to show that the interpretation of these experiments is really independent of the fair sampling assumption. For this purpose, we derive a more efficient Bell-type inequality which is a CHSH-type inequality in real experiments, using some alternative assumptions. Furthermore, Quantum mechanics violates our proposed inequality, In his celebrated 1964 paper, John Bell considered a system consisting of two spin-1 particles in a singlet state [1]. He showed that the correlation 2 between the results of two experiments done on such spatially separated particles
It is theoretically and experimentally shown that photons emitted by statistically independent incoherent classical light sources and measured in the far field in spatially separated modes may display spatial correlations akin to path-entanglement of photons produced by quantum sources. By measuring higher order photon-correlations at different locations, i.e., m photons in one mode and one photon in another mode, we experimentally demonstrate for m≥6 a violation of Bell-type inequalities for spatial degrees of freedom. The spatial correlations among the photons can be understood from state projection where the detection of the first m photons projects the sources onto a state which emits the subsequent photon in a strongly correlated manner. From this perspective the entanglement and violation of Bell's inequalities appears as a consequence of nonvanishing cross correlations between noncommuting quadrature phase components of the two spatially separated fields after m photons have been recorded. In this way we show that classical systems may produce spatial field correlations violating local realistic theories.