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arXiv:1807.00918 · Physical Review A

Experimental measurement-dependent local Bell test with human free will

Yang Liu, Xiao Yuan, Cheng Wu, Weijun Zhang, Jian-Yu Guan, Jiaqiang Zhong, Hao Li, Minghan Li, Carlos Abellán, Morgan W. Mitchell, Sheng‐Cai Shi, Jingyun Fan, Lixing You, Zhen Wang, Xiongfeng Ma, Qiang Zhang, Jian-Wei Pan

Published Feb 15, 2019• 3 citations
arXivHTMLPDF

Abstract

A Bell test can rule out local realistic models and has potential applications in communication and information tasks. For example, a Bell's inequality violation can certify the presence of intrinsic randomness in measurement outcomes, which can be used to generate unpredictable random numbers. Nevertheless, a Bell test requires measurements that are chosen independently of environment in the test, as would be the case if the measurement setting choices were themselves intrinsically random. Such situation seems to create a ``bootstrapping problem'' recently addressed in the BIG Bell Test, a collection of various Bell tests using human choices. Here, we report in detail our experimental methods and results within the BIG Bell Test, specifically for a special type of Bell inequality, known as the measurement-dependent local inequality. With this inequality, even a small amount of measurement independence makes it possible to disprove local realistic models. The experiment utilizes human-generated random numbers in selecting the measurement settings and is implemented with space-like separation between two distant measurement sites. The experimental result violates a Bell's inequality, which cannot be explained by local hidden variable models with independence parameter (as defined in [G. P\"utz et al., Phys. Rev. Lett. 113, 190402 (2014)]) $l>0.10\ifmmode\pm\else\textpm\fi{}0.05$. This result further quantifies the degree to which a local hidden variable model would need to constrain human choices, if it is to reproduce the experimental results.

DOI
10.1103/physreva.99.022115

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A Bell test can rule out local realistic models and has potential applications in communication and information tasks. For example, a Bell's inequality violation can certify the presence of intrinsic randomness in measurement outcomes, which can be used to generate unpredictable random numbers. Nevertheless, a Bell test requires measurements that are chosen independently of environment in the test, as would be the case if the measurement setting choices were themselves intrinsically random. Such situation seems to create a ``bootstrapping problem'' recently addressed in the BIG Bell Test, a collection of various Bell tests using human choices. Here, we report in detail our experimental methods and results within the BIG Bell Test, specifically for a special type of Bell inequality, known as the measurement-dependent local inequality. With this inequality, even a small amount of measurement independence makes it possible to disprove local realistic models. The experiment utilizes human-generated random numbers in selecting the measurement settings and is implemented with space-like separation between two distant measurement sites. The experimental result violates a Bell's inequality, which cannot be explained by local hidden variable models with independence parameter (as defined in [G. P"utz et al., Phys. Rev. Lett. 113, 190402 (2014)]) l>0.10\ifmmode±\else\textpm\fi0.05l>0.10\ifmmode\pm\else\textpm\fi{}0.05l>0.10\ifmmode±\else\textpm\fi0.05. This result further quantifies the degree to which a local hidden variable model would need to constrain human choices, if it is to reproduce the experimental results.
Bell's inequality was originally derived under the assumption that experimenters are free to select detector settings independently of any local ``hidden variables'' that might affect the outcomes of measurements on entangled particles. This assumption has come to be known as ``measurement independence'' (also referred to as ``freedom of choice'' or ``settings independence''). For a two-setting, two-outcome Bell test, we derive modified Bell inequalities that relax measurement independence, for either or both observers, while remaining locally causal. We describe the loss of measurement independence for each observer using the parameters M1{M}_{1}M1​ and M2{M}_{2}M2​, as defined by Hall in 2010, and also by a more complete description that adds two new parameters, which we call $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{{M}_{1}}$ and $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{{M}_{2}}$, deriving a modified Bell inequality for each description. These ``relaxed'' inequalities subsume those considered in previous work as special cases, and quantify how much the assumption of measurement independence needs to be relaxed in order for a locally causal model to produce a given violation of the standard Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequality. We show that both relaxed Bell inequalities are tight bounds on the CHSH parameter by constructing locally causal models that saturate them. For any given Bell inequality violation, the new two-parameter and four-parameter models each require significantly less mutual information between the hidden variables and measurement settings than previous models. We conjecture that the new models, with optimal parameters, require the minimum possible mutual information for a given Bell violation. We further argue that, contrary to various claims in the literature, relaxing freedom of choice need not imply superdeterminism.
Bell's theorem states that some predictions of quantum mechanics cannot be reproduced by a local-realist theory. That conflict is expressed by Bell's inequality, which is usually derived under the assumption that there are no statistical correlations between the choices of measurement settings and anything else that can causally affect the measurement outcomes. In previous experiments, this "freedom of choice" was addressed by ensuring that selection of measurement settings via conventional "quantum random number generators" was spacelike separated from the entangled particle creation. This, however, left open the possibility that an unknown cause affected both the setting choices and measurement outcomes as recently as mere microseconds before each experimental trial. Here we report on a new experimental test of Bell's inequality that, for the first time, uses distant astronomical sources as "cosmic setting generators." In our tests with polarization-entangled photons, measurement settings were chosen using real-time observations of Milky Way stars while simultaneously ensuring locality. Assuming fair sampling for all detected photons, and that each stellar photon's color was set at emission, we observe statistically significant ≳7.31σ and ≳11.93σ violations of Bell's inequality with estimated p values of ≲1.8×10^{-13} and ≲4.0×10^{-33}, respectively, thereby pushing back by ∼600 years the most recent time by which any local-realist influences could have engineered the observed Bell violation.
Quantum theory is inconsistent with any local hidden variable model as was first shown by Bell. To test Bell inequalities two separated observers extract correlations from a common ensemble of identical systems. Since quantum theory does not allow simultaneous measurements of noncommuting observables, on each system every party measures a single randomly chosen observable out of a given set. Here we suggest a different approach for testing Bell inequalities that is experimentally realizable by current methods. We show that Bell inequalities can be maximally violated even when all observables are measured on each member of the ensemble. This is possible by using weak measurements that produce small disturbance, at the expense of accuracy. However, our approach does not constitute an independent test of quantum nonlocality since the local hidden variables may correlate the noise of the measurement instruments. Nevertheless, by adding a randomly chosen precise measurement at the end of every cycle of weak measurements, the parties can verify that the hidden variables were not interfering with the noise, and thus validate the suggested test.
Bell's inequalities impose an upper limit on correlations between measurements of two-photon states under the assumption that the photons play by a set of local rules rather than by quantum mechanics. Quantum theory and decades of experiments both violate this limit. Recent theoretical work in quantum foundations has demonstrated that a local realist model can explain the non-local correlations observed in experimental tests of Bell's inequality if the underlying probability distribution of the local hidden variable depends on the choice of measurement basis, or ``setting choice''. By using setting choices determined by astrophysical events in the distant past, it is possible to asymptotically guarantee that the setting choice is independent of local hidden variables which come into play around the time of the experiment, closing this ``freedom-of-choice'' loophole. Here, I report on a novel experimental test of Bell's inequality which addresses the freedom-of-choice assumption more conclusively than any other experiment to date. In this first experiment in Vienna, custom astronomical instrumentation allowed setting choices to be determined by photon emission events occurring six hundred years ago at Milky Way stars. For this experiment, I selected the stars used to maximize the extent over which any hidden influence needed to be coordinated. In addition, I characterized the group's custom instrumentation, allowing us to conclude a violation of local realism by 777 and 111111 standard deviations. These results are published in Handsteiner et. al. (\textit{Phys. Rev. Lett.} 118:060401, 2017). I also describe my design, construction, and experimental characterization of a next-generation ``astronomical random number generator'', with improved capabilities and design choices that result in an improvement on the original instrumentation by an order of magnitude. Through the 1-meter telescope at the NASA/JPL Table Mountain Observatory, I observed and generated random bits from thirteen quasars with redshifts ranging from z=0.1−3.9z = 0.1-3.9z=0.1−3.9. With physical and information-theoretic analyses, I quantify the fraction of the generated bits which are predictable by a local realist mechanism, and identify two pairs of quasars suitable for use as extragalactic sources of randomness in the next cosmic Bell test. I also propose two additional applications of such a device. The first is an experimental realization of a delayed-choice quantum eraser experiment, enabling a foundational test of wave-particle complementarity. The second is a test of the Weak Equivalence Principle, using our instrument's sub-nanosecond time resolution to observe the Crab pulsar at optical and near-infrared wavelengths. Using my data from the Crab Pulsar, I report a bound on violations of Einstein's Weak Equivalence Principle complementary to recent results in the literature. Most of these results appear in Leung et. al. (arXiv:1706.02276, submitted to \textit{Physical Review X}).
It is well known that the effect of quantum nonlocality, as witnessed by violation of a Bell inequality, can be observed even when relaxing the assumption of measurement independence, i.e., allowing for the source to be partially correlated with the choices of measurement settings; however, what is the minimal amount of measurement independence needed to observe quantum nonlocality? Here we explore this question and consider models with strong measurement-dependent locality, where measurement choices can be perfectly determined in almost all rounds of the Bell test. Nevertheless, we show that quantum nonlocality can still be observed in this scenario, which we conjecture is minimal within the framework we use. We also discuss potential applications in randomness amplification.
Loophole-free violations of Bell inequalities imply that at least one of the assumptions behind local hidden-variable theories must fail. Here, we show that, if only one fails, then it has to fail completely, therefore excluding models that partially constrain freedom of choice or allow for partial retrocausal influences, or allow partial instantaneous actions at a distance. Specifically, we show that (i) any hidden-variable theory with outcome independence (OI) and arbitrary joint relaxation of measurement independence (MI) and parameter independence (PI) can be experimentally excluded in a Bell-like experiment with many settings on high-dimensional entangled states, and (ii) any hidden-variable theory with MI, PI and arbitrary relaxation of OI can be excluded in a Bell-like experiment with many settings on qubit-qubit entangled states. Loophole-free violations of Bell inequalities imply that at least one of the assumptions formalising local hidden-variable theories must fail. Here, the authors show that, if only one is false, then it has to fail completely, therefore excluding models that allow partial instantaneous actions at a distance, partially constrain freedom of choice or allow for partial retrocausal influences.