An active area of research in the fields of machine learning and statistics is the development of causal discovery algorithms, the purpose of which is to infer the causal relations that hold among a ...set of variables from the correlations that these exhibit . We apply some of these algorithms to the correlations that arise for entangled quantum systems. We show that they cannot distinguish correlations that satisfy Bell inequalities from correlations that violate Bell inequalities, and consequently that they cannot do justice to the challenges of explaining certain quantum correlations causally. Nonetheless, by adapting the conceptual tools of causal inference, we can show that any attempt to provide a causal explanation of nonsignalling correlations that violate a Bell inequality must contradict a core principle of these algorithms, namely, that an observed statistical independence between variables should not be explained by fine-tuning of the causal parameters. In particular, we demonstrate the need for such fine-tuning for most of the causal mechanisms that have been proposed to underlie Bell correlations, including superluminal causal influences, superdeterminism (that is, a denial of freedom of choice of settings), and retrocausal influences which do not introduce causal cycles.
Local realism is the worldview in which physical properties of objects exist independently of measurement and where physical influences cannot travel faster than the speed of light. Bell's theorem ...states that this worldview is incompatible with the predictions of quantum mechanics, as is expressed in Bell's inequalities. Previous experiments convincingly supported the quantum predictions. Yet, every experiment requires assumptions that provide loopholes for a local realist explanation. Here, we report a Bell test that closes the most significant of these loopholes simultaneously. Using a well-optimized source of entangled photons, rapid setting generation, and highly efficient superconducting detectors, we observe a violation of a Bell inequality with high statistical significance. The purely statistical probability of our results to occur under local realism does not exceed 3.74×10^{-31}, corresponding to an 11.5 standard deviation effect.
What Bell did Maudlin, Tim
Journal of physics. A, Mathematical and theoretical,
10/2014, Letnik:
47, Številka:
42
Journal Article
Recenzirano
Odprti dostop
On the 50th anniversary of Bell's monumental 1964 paper, there is still widespread misunderstanding about exactly what Bell proved. This misunderstanding derives in turn from a failure to appreciate ...the earlier argument of Einstein, Podolsky and Rosen. I retrace the history and logical structure of these arguments in order to clarify the proper conclusion, namely that any world that displays violations of Bell's inequality for experiments done far from one another must be non-local. Since the world we happen to live in displays such violations, actual physics is non-local. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to '50 years of Bell's theorem'.
More randomness from the same data Bancal, Jean-Daniel; Sheridan, Lana; Scarani, Valerio
New journal of physics,
03/2014, Letnik:
16, Številka:
3
Journal Article
Recenzirano
Odprti dostop
Correlations that cannot be reproduced with local variables certify the generation of private randomness. Usually, the violation of a Bell inequality is used to quantify the amount of randomness ...produced. Here, we show how private randomness generated during a Bell test can be directly quantified from the observed correlations, without the need to process these data into an inequality. The frequency with which the different measurement settings are used during the Bell test can also be taken into account. This improved analysis turns out to be very relevant for Bell tests performed with a finite collection efficiency. In particular, applying our technique to the data of a recent experiment (Christensen et al 2013 Phys. Rev. Lett. 111 130406), we show that about twice as much randomness as previously reported can be potentially extracted from this setup.
The bell regression is used, when the response variable is in the form of counts with over dispersion. The bell regression coefficients are generally estimated using the maximum likelihood estimator ...(MLE). It is known that the performance of the traditional MLE is very sensitive to multicollinearity. Therefore, we propose a Bell ridge regression (BRR) as a solution to the multicollinearity problems. For the assessment of BRR, we conduct a Monte Carlo simulation study to monitor the performance of the proposed estimator where the mean squared error (MSE) is considered as an evaluation criterion. Also, two real examples are included to show the superiority of the BRR estimator.
The majority of recent works investigating the link between non-locality and randomness, e.g. in the context of device-independent cryptography, do so with respect to some specific Bell inequality, ...usually the CHSH inequality. However, the joint probabilities characterizing the measurement outcomes of a Bell test are richer than just the degree of violation of a single Bell inequality. In this work we show how to take this extra information into account in a systematic manner in order to optimally evaluate the randomness that can be certified from non-local correlations. We further show that taking into account the complete set of outcome probabilities is equivalent to optimizing over all possible Bell inequalities, thereby allowing us to determine the optimal Bell inequality for certifying the maximal amount of randomness from a given set of non-local correlations.
Strong Loophole-Free Test of Local Realism Shalm, Lynden K; Meyer-Scott, Evan; Christensen, Bradley G ...
Physical review letters,
2015-Dec-18, Letnik:
115, Številka:
25
Journal Article
Recenzirano
Odprti dostop
We present a loophole-free violation of local realism using entangled photon pairs. We ensure that all relevant events in our Bell test are spacelike separated by placing the parties far enough apart ...and by using fast random number generators and high-speed polarization measurements. A high-quality polarization-entangled source of photons, combined with high-efficiency, low-noise, single-photon detectors, allows us to make measurements without requiring any fair-sampling assumptions. Using a hypothesis test, we compute p values as small as 5.9×10^{-9} for our Bell violation while maintaining the spacelike separation of our events. We estimate the degree to which a local realistic system could predict our measurement choices. Accounting for this predictability, our smallest adjusted p value is 2.3×10^{-7}. We therefore reject the hypothesis that local realism governs our experiment.
PDF
