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arXiv:2007.07656 · Physical Review A

Holographically controlled random numbers from entangled twisted photons

Michael De Oliveira, Nicholas Bornman, Andrew Forbes

Published Sep 21, 2020• 4 citations
arXivHTMLPDF

Abstract

We present a quantum random number generator (QRNG) based on the random outcomes inherent in projective measurements on a superposition of quantum states of light. First, we use multiplexed holograms encoded on a spatial light modulator to spatially map down-converted photons onto a superposition of optical paths. This gives us full digital control of the mapping process which we can tailor to achieve any desired probability distribution. More importantly, we use this method to account for any bias present within our transmission and detection system, forgoing the need for time-consuming and inefficient unbiasing algorithms. Our QRNG achieved a min-entropy of ${H}_{\text{min}}=0.9991\ifmmode\pm\else\textpm\fi{}0.0003$ bits per photon and passed the NIST Statistical Test Suite. Furthermore, we extend our approach to realize a QRNG based on photons entangled in their orbital angular momentum (OAM) degree of freedom. This combination of digital holograms and projective measurements on arbitrary OAM combinations allowed us to generate random numbers with arbitrary distributions, in effect tailoring the system's entropy while maintaining the inherent quantum irreproducibility. Such techniques allow access to the higher-dimensional OAM Hilbert space, opening up an avenue for generating multiple random bits per photon.

DOI
10.1103/physreva.102.032620

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We present a quantum random number generator (QRNG) based on the random outcomes inherent in projective measurements on a superposition of quantum states of light. First, we use multiplexed holograms encoded on a spatial light modulator to spatially map down-converted photons onto a superposition of optical paths. This gives us full digital control of the mapping process which we can tailor to achieve any desired probability distribution. More importantly, we use this method to account for any bias present within our transmission and detection system, forgoing the need for time-consuming and inefficient unbiasing algorithms. Our QRNG achieved a min-entropy of Hmin=0.9991\ifmmode±\else\textpm\fi0.0003{H}_{\text{min}}=0.9991\ifmmode\pm\else\textpm\fi{}0.0003Hmin​=0.9991\ifmmode±\else\textpm\fi0.0003 bits per photon and passed the NIST Statistical Test Suite. Furthermore, we extend our approach to realize a QRNG based on photons entangled in their orbital angular momentum (OAM) degree of freedom. This combination of digital holograms and projective measurements on arbitrary OAM combinations allowed us to generate random numbers with arbitrary distributions, in effect tailoring the system's entropy while maintaining the inherent quantum irreproducibility. Such techniques allow access to the higher-dimensional OAM Hilbert space, opening up an avenue for generating multiple random bits per photon.
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Abstract Measurement outcomes on quantum systems exhibit inherent randomness and are fundamentally nondeterministic. This has enabled quantum physics to set new standards for the generation of true randomness with significant applications in the fields of cryptography, statistical simulations, and modeling of the nondeterministic behavior in various other fields. In this work, we present a scheme for the generation of multi-bit random numbers using path-entangled single photons. For the experimental demonstration, we generate a path-entangled state using single photons from spontaneous parametric down-conversion (SPDC) and assign a multi-qubit state for them in path basis. One-bit and two-bit random numbers are then generated by measuring entangled states in the path basis. In addition to passing the NIST tests for randomness, we also demonstrate the certification of quantumness and self-certification of quantum random number generator (QRNG) using Clauser, Horne, Shimony and Holt (CHSH) inequality violation. We also record the significantly low autocorrelation coefficient from the raw bits generated and this along with CHSH violation rules out multi-photon events and ensure the protection from photon splitting attack. Distribution of photons along multiple paths resulting in multiple bits from one photon extends the limit on bit generation rate imposed by the detection dead time of the individual detector. Thus, the path-entangled states can generate higher bitrates compared to scheme using entangled photon pair which are limited by the coincidence counts. We demonstrate this by generating a high rate of about 80 Mbps when the single photon detector saturates at around 28 Mcps and still show violation of CHSH inequality.
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Abstract Quantum random number generators (QRNGs) are based on naturally random measurement results performed on individual quantum systems. Here, we demonstrate a branching-path photonic QRNG implemented using a Sagnac interferometer with a tunable splitting ratio. The fine-tuning of the splitting ratio allows us to maximize the entropy of the generated sequence of random numbers and effectively compensate for tolerances in the components. By producing single-photons from attenuated telecom laser pulses, and employing commercially-available components we are able to generate a sequence of more than 2 gigabytes of random numbers with an average entropy of 7.99 bits/byte directly from the raw measured data. Furthermore, our sequence passes randomness tests from both the NIST and Dieharder statistical test suites, thus certifying its randomness. Our scheme shows an alternative design of QRNGs based on the dynamic adjustment of the uniformity of the produced random sequence, which is relevant for the construction of modern generators that rely on independent real-time testing of its performance.
Random Number Generators (QRNGs) represent a promising alternative to classical pseudorandom methods, providing a genuine source of randomness based on the fundamental principles of quantum mechanics.This article investigates a particular class of QRNGs -Optical Quantum Random Number Generators (OQRNGs) -which rely on phenomena such as quantum state superposition, wavefunction collapse, vacuum fluctuations, and Raman scattering to generate random bits.The architecture of these systems is analyzed in detail, along with the types of photon sources and detectors employed, as well as the entropy extraction mechanisms.Through a comparative approach, the advantages and limitations of each technology are highlighted: from the simplicity of implementation in beam-splitter-based generators to the high bit rates and scalability offered by systems using homodyne detection or Raman-based schemes.The study results indicate that OQRNGs can be successfully integrated into critical post-quantum security infrastructures, providing verifiable randomness that is fundamentally irreproducible by algorithmic means.In conclusion, optical quantum random number generators constitute a key step toward enhancing digital security by directly harnessing the fundamental uncertainty inherent in the physical nature of light.
The experimental realization of multidimensional quantum states may lead to unexplored and interesting physics, as well as advanced quantum communication protocols. The orbital angular momentum of photons is a well suitable discrete degree of freedom for implementing high-dimensional quantum systems. The standard method to generate and manipulate such photon modes is to use bulk and fixed optics. Here the authors demonstrate the utilization of a spatial light modulator to manipulate the orbital angular momentum of entangled photons generated in spontaneous parametric downconversion. They show that their setup allows them to realize photonic entanglement of up to 21 dimensions, which in principle can be extended to even larger dimensions.