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arXiv:1706.02276 · Physical Review A

Astronomical random numbers for quantum foundations experiments

Calvin Leung, Amy E. Brown, Hien Nguyen, Andrew S. Friedman, David I. Kaiser, Jason R. Gallicchio

Published Apr 24, 2018• 16 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.97.042120

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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.
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}).
We propose a practical scheme to use photons from causally disconnected cosmic sources to set the detectors in an experimental test of Bell's inequality. In current experiments, with settings determined by quantum random number generators, only a small amount of correlation between detector settings and local hidden variables, established less than a millisecond before each experiment, would suffice to mimic the predictions of quantum mechanics. By setting the detectors using pairs of quasars or patches of the cosmic microwave background, observed violations of Bell's inequality would require any such coordination to have existed for billions of years-an improvement of 20 orders of magnitude.
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.
Viewing two astronomical sources at large enough distance and angular separation can assure, by light-travel-time arguments, the acausality of their emitted photons. Using such photons to set apparatus parameters in a laboratory-based quantum-mechanical experiment could ensure those switch settings are independent and fair, allowing a loophole-free test of Bell's inequality. Quasars are a natural choice for this task, yet at ultimate extent it involves their simultaneous photometry towards opposite directions on the sky, which is untried. Cosmic isotropy can be invoked to set limits there, leaving fairness intact for causal pairs, but with a testable consequence of asymmetric bias: mean brightness correlations found less flat in sky angle than random, more acutely so inside a horizon of 90 degrees. Analysis of one dataset from the Gemini twin telescopes is presented, using over 14 years of archival broadband-optical images, serendipitously sampling thousands of quasars up to 180 degrees apart. These data reject a null result of no correlation with 97.7% confidence, instead consistent with a 3-sigma residual signal of 0.21 mag peaked at 65+/-3 degrees separation. Possible confirmatory observations are pointed to along with the improved experimental protocol of an Earth-wide test.
In this Letter, we present a cosmic Bell experiment with polarization-entangled photons, in which measurement settings were determined based on real-time measurements of the wavelength of photons from high-redshift quasars, whose light was emitted billions of years ago; the experiment simultaneously ensures locality. Assuming fair sampling for all detected photons and that the wavelength of the quasar photons had not been selectively altered or previewed between emission and detection, we observe statistically significant violation of Bell's inequality by 9.3 standard deviations, corresponding to an estimated p value of ≲7.4×10^{-21}. This experiment pushes back to at least ∼7.8 Gyr ago the most recent time by which any local-realist influences could have exploited the "freedom-of-choice" loophole to engineer the observed Bell violation, excluding any such mechanism from 96% of the space-time volume of the past light cone of our experiment, extending from the big bang to today.
Random numbers are indispensable for a variety of applications ranging from testing physics foundations to information encryption. In particular, nonlocality test provide strong evidence for our current understanding of nature-quantum mechanics. All the random number generators (RNGs) used for the existing tests are constructed locally, making the test results vulnerable to the freedom-of-choice loophole. We report an experimental realization of RNGs based on the arrival time of cosmic photons. The measurement outcomes (raw data) pass the standard NIST statistical test suite. We present a realistic design to employ these RNGs in a Bell test experiment, which addresses the freedom-of-choice loophole.