# Quantum Random Number Generation Using a Quanta Image Sensor

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Randomness Generation Concept

_{n}(e− r.m.s.). The result is a sum of constituent PDF components, one for each possible value of k and weighted by the Poisson probability for that k [11]:

_{n}above 1 e− r.m.s., where the photon-counting peaks of Figure 1 are fully “blurred” by noise (e.g., conventional CMOS image sensors), the optimum settings of ${U}_{t}$ and H converge so that the resultant Gaussian readout signal PDF is split in half at the peak, as one might deduce intuitively.

## 3. Data Collection

## 4. Results

_{n}= 0.24 e− r.m.s. Then we used the obtained value in the formula of the probability that the extractor output will deviate from a perfectly uniform q-bit string:

## 5. Comparison with Other Technologies

## 6. Summary

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Stefanov, A.; Gisin, N.; Guinnard, O.; Guinnard, L.; Zbinden, H. Optical quantum random number generator. J. Modern Opt.
**2000**, 47, 595–598. [Google Scholar] [CrossRef] - Dultz, W.; Hidlebrandt, E. Optical Random-Number Generator Based on Single-Photon Statistics at the Optical Beam Splitter. U.S. Patent No. 6,393,448, 21 May 2002. [Google Scholar]
- Wei, W.; Guo, H. Bias-Free true random-number generator. Opt. Lett.
**2009**, 34, 1876–1878. [Google Scholar] [CrossRef] [PubMed] - Gabriel, C.; Wittmann, C.; Sych, D.; Dong, R.; Mauerer, W.; Andersen, U.L.; Marquardt, C.; Leuchs, G. A generator for unique quantum random numbers based on vacuum states. Nat. Photonics
**2010**, 4, 711–715. [Google Scholar] [CrossRef] - Shen, Y.; Tian, L.A.; Zou, H.X. Practical quantum random number generator based on measuring the shot noise of vacuum states. Phys. Rev.
**2010**, 61. [Google Scholar] [CrossRef] - Sanguinetti, B.; Martin, A.; Zbinden, H.; Gisin, N. Quantum random number generation on a mobile phone. Phys. Rev.
**2014**, 4. [Google Scholar] [CrossRef] - Fossum, E.R. The quanta image sensor (QIS): Concepts and challenges. In Proceedings of the 2011 Optical Society of America Topical Meeting on Computational Optical Sensing and Imaging, Toronto, ON, Canada, 10–14 July 2011.
- Masoodian, S.; Rao, A.; Ma, J.; Odame, K.; Fossum, E.R. A 2.5 pJ/b binary image sensor as a pathfinder for quanta image sensors. IEEE Trans. Electron. Devices
**2015**, 63, 100–105. [Google Scholar] [CrossRef] - Fossum, E.R. Modeling the performance of single-bit and multi-bit quanta image sensors. IEEE J. Electron. Devices Soc.
**2013**, 1, 166–174. [Google Scholar] [CrossRef] - Fossum, E.R. Application of photon statistics to the quanta image sensor. In Proceedings of the International Image Sensor Workshop (IISW), Snowbird Resort, UT, USA, 12–16 June 2013.
- Fossum, E.R. Photon counting error rates in single-bit and multi-bit quanta image sensors. IEEE J. Electron. Devices Soc.
**2016**. [Google Scholar] [CrossRef] - Ma, J.; Fossum, E.R. Quanta image sensor jot with sub 0.3 e− r.m.s. read noise. IEEE Electron. Device Lett.
**2015**, 36, 926–928. [Google Scholar] [CrossRef] - Ma, J.; Starkey, D.; Rao, A.; Odame, K.; Fossum, E.R. Characterization of quanta image sensor pump-gate jots with deep sub-electron read noise. IEEE J. Electron. Devices Soc.
**2015**, 3, 472–480. [Google Scholar] [CrossRef] - Ma, J.; Fossum, E.R. A pump-gate jot device with high conversion gain for a Quanta Image Sensor. IEEE J. Electron. Devices Soc.
**2015**, 3, 73–77. [Google Scholar] [CrossRef] - Starkey, D.; Fossum, E.R. Determining conversion gain and read noise using a photon-counting histogram method for deep sub-electron read noise image sensors. IEEE J. Electron. Devices Soc.
**2016**. [Google Scholar] [CrossRef] - Shannon, C.E. A mathematical theory of communication. Bell Syst. Tech. J.
**1948**, 3, 379–423. [Google Scholar] [CrossRef] - Troyer, M.; Renner, R. A Randomness Extractor for the Quantis Device, ID Quantique. Available online: http://www.idquantique.com/wordpress/wp-content/uploads/quantis-rndextract-techpaper.pdf (accessed on 27 June 2016).
- Rukhin, A.; Soto, J.; Nechvatal, J.; Smid, M.; Barker, E. A Statistical Rest Suite for Random and Pseudorandom Number Generators for Cryptographic Applications. National Institute of Standards and Technology (NIST), Special Pub. 800-22, 15 May 2001. Available online: http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA393366 (accessed on 27 June 2016).
- Stucki, D.; Burri, S.; Charbon, E.; Chunnilall, C.; Meneghetti, A.; Regazzoni, F. Towards a high-speed quantum random number generator. Proc. SPIE
**2013**, 8899. [Google Scholar] [CrossRef] - Tisa, S.; Villa, F.; Giudice, A.; Simmerle, G.; Zappa, F. High-Speed quantum random number generation using CMOS photon counting detectors. IEEE J. Sel. Top. Quant. Electron.
**2015**, 21. [Google Scholar] [CrossRef]

**Figure 1.**Readout signal probability distribution function (PDF) from Poisson distribution corrupted with read noise. Quanta exposure H = 0.7 and read noise u

_{n}= 0.24 e− r.m.s.

**Figure 2.**Cumulative probability of readout signal with read noise u

_{n}= 0.24 e− r.m.s. and quanta exposure H = 0.7.

**Figure 3.**Binary data entropy variation caused by quanta exposure fluctuation during data collection.

**Figure 6.**Quanta exposure fluctuation during data collection. Each dataset contains 1,000,000 samples.

Criteria | QIS | CIS | SPADs Matrix |
---|---|---|---|

Data Rate ^{1} | 5–12 Gb/s | 0.3–1 Gb/s | 0.1–0.6 Gb/s |

Read Noise | <0.25 e− r.m.s. | >1 e− r.m.s. | <0.15 e− r.m.s. |

Dark Current/Count Rate ^{2} | 0.1 e−/(jot·s) | 10–500 e−/(pix·s) | 200 counts/(pix·s) |

Power Supply | 2.5/3.3 V | 2.5/3.3/5 V | 22–27 V |

Single Photon Counting | YES | NO | YES |

^{1}For a device with 2.5 mm

^{2}area size;

^{2}We define Dark Current for QIS/CIS and Dark Count Rate for SPADs, these values are measured at room temperature.

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Amri, E.; Felk, Y.; Stucki, D.; Ma, J.; Fossum, E.R.
Quantum Random Number Generation Using a Quanta Image Sensor. *Sensors* **2016**, *16*, 1002.
https://doi.org/10.3390/s16071002

**AMA Style**

Amri E, Felk Y, Stucki D, Ma J, Fossum ER.
Quantum Random Number Generation Using a Quanta Image Sensor. *Sensors*. 2016; 16(7):1002.
https://doi.org/10.3390/s16071002

**Chicago/Turabian Style**

Amri, Emna, Yacine Felk, Damien Stucki, Jiaju Ma, and Eric R. Fossum.
2016. "Quantum Random Number Generation Using a Quanta Image Sensor" *Sensors* 16, no. 7: 1002.
https://doi.org/10.3390/s16071002