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We show that paradoxical consequences of violations of Bells inequality are induced by the use of an unsuitable probabilistic description for the EPR-Bohm-Bell experiment. The conventional description (due to Bell) is based on a combination of statistical data collected for different settings of polarization beam splitters (PBSs). In fact, such data consists of some conditional probabilities which only partially define a probability space. Ignoring this conditioning leads to apparent contradictions in the classical probabilistic model (due to Kolmogorov). We show how to make a completely consistent probabilistic model by taking into account the probabilities of selecting the settings of the PBSs. Our model matches both the experimental data and is consistent with classical probability theory.
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We show that the projection postulate plays a crucial role in the discussion on the so called quantum nonlocality, in particular in the EPR-argument. We stress that the original von Neumann projection postulate was crucially modified by extending it to observables with degenerate spectra (the Luders postulate) and we show that this modification is highly questionable from a physical point of view, and it is the real source of quantum nonlocality. The use of the original von Neumann postulate eliminates this problem: instead of action at the distance-nonlocality, we obtain a classical measurement nonlocality. It seems that EPR did mistake in their 1935-paper: if one uses correctly von Neumann projection postulate, no ``elements of reality can be assigned to entangled systems. Our analysis of the EPR and projection postulate makes clearer Bohrs considerations in his reply to Einstein.
The appearance of the spin-1/2 and spin-1 representations in the Frieden-Soffer extreme physical information (EPI) statistical approach to the Einstein-Podolsky-Rosen-Bohm (EPR-Bohm) experiment is shown. In order to obtain the EPR-Bohm result, in addition to the observed structural and variational information principles of the EPI method, the condition of the regularity of the probability distribution is used. The observed structural information principle is obtained from the analyticity of the logarithm of the likelihood function. It is suggested that, due to the self-consistent analysis of both information principles, quantum mechanics is covered by the statistical information theory. The estimation of the angle between the analyzers in the EPR-Bohm experiment is discussed.
The detection of nonlocal correlations in a Bell experiment implies almost by definition some intrinsic randomness in the measurement outcomes. For given correlations, or for a given Bell violation, the amount of randomness predicted by quantum physics, quantified by the guessing probability, can generally be bounded numerically. However, currently only a few exact analytic solutions are known for violations of the bipartite Clauser-Horne-Shimony-Holt Bell inequality. Here, we study the randomness in a Bell experiment where three parties test the tripartite Mermin-Bell inequality. We give tight upper bounds on the guessing probabilities associated with one and two of the parties measurement outcomes as a function of the Mermin inequality violation. Finally, we discuss the possibility of device-independent secret sharing based on the Mermin inequality and argue that the idea seems unlikely to work.
The non-local correlations exhibited when measuring entangled particles can be used to certify the presence of genuine randomness in Bell experiments. While non-locality is necessary for randomness certification, it is unclear when and why non-locality certifies maximal randomness. We provide here a simple argument to certify the presence of maximal local and global randomness based on symmetries of a Bell inequality and the existence of a unique quantum probability distribution that maximally violates it. Using our findings, we prove the existence of N-party Bell test attaining maximal global randomness, that is, where a combination of measurements by each party provides N perfect random bits.
Entanglement is the defining feature of quantum mechanics, and understanding the phenomenon is essential at the foundational level and for future progress in quantum technology. The concept of steering was introduced in 1935 by Schrodinger as a generalization of the Einstein-Podolsky-Rosen (EPR) paradox. Surprisingly, it has only recently been formalized as a quantum information task with arbitrary bipartite states and measurements, for which the existence of entanglement is necessary but not sufficient. Previous experiments in this area have been restricted to the approach of Reid [PRA 40, 913], which followed the original EPR argument in considering only two different measurement settings per side. Here we implement more than two settings so as to be able to demonstrate experimentally, for the first time, that EPR-steering occurs for mixed entangled states that are Bell-local (that is, which cannot possibly demonstrate Bell-nonlocality). Unlike the case of Bell inequalities, increasing the number of measurement settings beyond two--we use up to six--dramatically increases the robustness of the EPR-steering phenomenon to noise.
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