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arXiv:1510.00248

Random 'choices' and the locality loophole

Stefano Pironio

Published Oct 1, 2015• 34 citations
arXivHTMLPDF

Abstract

It has been claimed that to close the locality loophole in a Bell experiment, random numbers of quantum origin should be used for selecting the measurement settings. This is how it has been implemented in all recent Bell experiment addressing this loophole. I point out in this note that quantum random number generators are unnecessary for such experiments and that a Bell experiment with a pseudo-random (but otherwise completely deterministic) mechanism for selecting the measurement settings, such as taking a hash function of the latest million tweets with the hashtag #quantum, would be as convincing, or even more, than one using quantum random number generators.

DOI
10.48550/arxiv.1510.00248

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It has been claimed that to close the locality loophole in a Bell experiment, random numbers of quantum origin should be used for selecting the measurement settings. This is how it has been implemented in all recent Bell experiment addressing this loophole. I point out in this note that quantum random number generators are unnecessary for such experiments and that a Bell experiment with a pseudo-random (but otherwise completely deterministic) mechanism for selecting the measurement settings, such as taking a hash function of the latest million tweets with the hashtag #quantum, would be as convincing, or even more, than one using quantum random number generators.
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}).
Many experimental setups in quantum physics use pseudorandomness in places where the theory requires randomness. In this Letter we show that the use of pseudorandomness instead of proper randomness in quantum setups has potentially observable consequences. First, we present a new loophole for Bell-like experiments: if some of the parties choose their measurements pseudorandomly, then the computational resources of the local model have to be limited in order to have a proper observation of nonlocality. Second, we show that no amount of pseudorandomness is enough to produce a mixed state by computably choosing pure states from some basis.
Recent experiments have reached detection efficiencies sufficient to close the detection loophole with photons. Both experiments ran multiple successive trials in fixed measurement configurations, rather than randomly re-setting the measurement configurations before each measurement trial. This opens a new potential loophole for a local hidden variable theory. The loophole invalidates one proposed method of statistical analysis of the experimental results, as demonstrated in this note. Therefore a different analysis will be necessary to definitively assert that these experiments are subject only to the locality loophole.
Photons from distant astronomical sources can be used as a classical source of randomness to improve fundamental tests of quantum nonlocality, wave-particle duality, and local realism through Bell's inequality and delayed-choice quantum eraser tests inspired by Wheeler's cosmic-scale Mach-Zehnder interferometer gedanken experiment.Such sources of random numbers may also be useful for information-theoretic applications such as key distribution for quantum cryptography.Building on the design of an astronomical random number generator developed for the recent cosmic Bell experiment [Handsteiner et al.Phys. Rev. Lett. 118, 060401 (2017)], in this paper we report on the design and characterization of a device that, with 20-nanosecond latency, outputs a bit based on whether the wavelength of an incoming photon is greater than or less than ≈700 nm.Using the one-meter telescope at the Jet Propulsion Laboratory Table Mountain Observatory, we generated random bits from astronomical photons in both color channels from 50 stars of varying color and magnitude, and from 12 quasars with redshifts up to z = 3.9.With stars, we achieved bit rates of ∼1 × 10 6 Hz/m 2 , limited by saturation of our single-photon detectors, and with quasars of magnitudes between 12.9 and 16, we achieved rates between ∼10 2 and 2 × 10 3 Hz/m 2 .For bright quasars, the resulting bitstreams exhibit sufficiently low amounts of statistical predictability as quantified by the mutual information.In addition, a sufficiently high fraction of bits generated are of true astronomical origin in order to address both the locality and freedom-of-choice loopholes when used to set the measurement settings in a test of the Bell-CHSH inequality.