# Astronomical random numbers for quantum foundations experiments

## 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, 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 $\approx 700$ 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 $~1\times {10}^{6}\phantom{\rule{0ex}{0ex}}{\mathrm{Hz}/\mathrm{m}}^{2}$, 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 $2\times {10}^{3}\phantom{\rule{0ex}{0ex}}\mathrm{Hz}/{\mathrm{m}}^{2}$. 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.

- Authors:

- Publication Date:

- Research Org.:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); California Institute of Technology (CalTech), Pasadena, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP); National Aeronautics and Space Administration (NASA); National Science Foundation (NSF)

- OSTI Identifier:
- 1434398

- Alternate Identifier(s):
- OSTI ID: 1503823

- Grant/Contract Number:
- SC0012567; PHY-1541160

- Resource Type:
- Published Article

- Journal Name:
- Physical Review A

- Additional Journal Information:
- Journal Name: Physical Review A Journal Volume: 97 Journal Issue: 4; Journal ID: ISSN 2469-9926

- Publisher:
- American Physical Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; quantum nonlocality; electromagnetic radiation astronomy

### Citation Formats

```
Leung, Calvin, Brown, Amy, Nguyen, Hien, Friedman, Andrew S., Kaiser, David I., and Gallicchio, Jason. Astronomical random numbers for quantum foundations experiments. United States: N. p., 2018.
Web. https://doi.org/10.1103/PhysRevA.97.042120.
```

```
Leung, Calvin, Brown, Amy, Nguyen, Hien, Friedman, Andrew S., Kaiser, David I., & Gallicchio, Jason. Astronomical random numbers for quantum foundations experiments. United States. https://doi.org/10.1103/PhysRevA.97.042120
```

```
Leung, Calvin, Brown, Amy, Nguyen, Hien, Friedman, Andrew S., Kaiser, David I., and Gallicchio, Jason. Tue .
"Astronomical random numbers for quantum foundations experiments". United States. https://doi.org/10.1103/PhysRevA.97.042120.
```

```
@article{osti_1434398,
```

title = {Astronomical random numbers for quantum foundations experiments},

author = {Leung, Calvin and Brown, Amy and Nguyen, Hien and Friedman, Andrew S. and Kaiser, David I. and Gallicchio, Jason},

abstractNote = {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, 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 ~1×106Hz/m2, limited by saturation of our single-photon detectors, and with quasars of magnitudes between 12.9 and 16, we achieved rates between ~102 and 2×103Hz/m2. 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},

journal = {Physical Review A},

number = 4,

volume = 97,

place = {United States},

year = {2018},

month = {4}

}

https://doi.org/10.1103/PhysRevA.97.042120

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*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*