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arXiv:2410.00440 · AVS Quantum Science

Beam-splitter-free, device-independent, high bit-rate, quantum random number generator based on temporal and spatial correlations of heralded single-photons

Ayan Kumar Nai, Amritash Sharma, Vimlesh Kumar, Sandeep Singh, Shreya V. Mishra, C. M. Chandrashekar, G. K. Samanta

Published Feb 13, 2025• 4 citations
arXivHTMLPDF

Abstract

Spontaneous parametric down-conversion (SPDC), an inherently random quantum process, produces pair photons with strong temporal and spatial correlations due to energy and momentum conservation, and acts as the key for quantum random number generation (QRNG). Standard QRNG methods primarily use temporal correlations with beam splitters, limiting bit rates. However, due to spatial correlation, the pair photons in non-collinear phase-matched SPDC-setup appear at diametrically opposite points on an annular spatial distribution. Therefore, exploring the temporal correlation between the spatially correlated photon-pairs from different sections of the annual ring can directly lead to device-independent, multi-bit QRNG at a high rate, eliminating the need of a physical object such as a beam splitter. As a proof-of-concept, we report on high-bit-rate QRNG by using spatial correlation of photon-pairs by sectioning the SPDC ring of a non-collinear, degenerate, high-brightness source and temporal correlation between the diametrically opposite sections. Dividing the annular ring of the high-brightness photon-pair source based on a 20-mm-long, type-0 phase-matched, periodically poled KTP crystal into four sections, recording the timestamp of the coincidences (window of 1 ns) between photons from diametrically opposite sections and assigning bits (0 and 1), we extracted 90 × 106 raw bits over 27.7 s at a pump power of 17 mW. Using minimum entropy evaluation, we determined an extraction ratio of over 95 % for raw bits. Further, using Toeplitz matrix-based post-processing, we developed QRNG with bit rate of 3 Mbps, passing all NIST 800-22 and TestU01 test suites. The generic scheme shows the possibility of further enhancement of bit rate with more sectioning of the SPDC ring.

DOI
10.1116/5.0245672

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Spontaneous parametric down-conversion (SPDC), an inherently random quantum process, produces pair photons with strong temporal and spatial correlations due to energy and momentum conservation, and acts as the key for quantum random number generation (QRNG). Standard QRNG methods primarily use temporal correlations with beam splitters, limiting bit rates. However, due to spatial correlation, the pair photons in non-collinear phase-matched SPDC-setup appear at diametrically opposite points on an annular spatial distribution. Therefore, exploring the temporal correlation between the spatially correlated photon-pairs from different sections of the annual ring can directly lead to device-independent, multi-bit QRNG at a high rate, eliminating the need of a physical object such as a beam splitter. As a proof-of-concept, we report on high-bit-rate QRNG by using spatial correlation of photon-pairs by sectioning the SPDC ring of a non-collinear, degenerate, high-brightness source and temporal correlation between the diametrically opposite sections. Dividing the annular ring of the high-brightness photon-pair source based on a 20-mm-long, type-0 phase-matched, periodically poled KTP crystal into four sections, recording the timestamp of the coincidences (window of 1 ns) between photons from diametrically opposite sections and assigning bits (0 and 1), we extracted 90 × 106 raw bits over 27.7 s at a pump power of 17 mW. Using minimum entropy evaluation, we determined an extraction ratio of over 95 % for raw bits. Further, using Toeplitz matrix-based post-processing, we developed QRNG with bit rate of 3 Mbps, passing all NIST 800-22 and TestU01 test suites. The generic scheme shows the possibility of further enhancement of bit rate with more sectioning of the SPDC ring.
Device-independent quantum random number generators (DI-QRNGs) are crucial for many information-processing applications, requiring certified quantumness to ensure genuine randomness. However, inherent technical challenges in implementing quantumness tests often result in a low bit rate. Here, we present a high-bit-rate DI-QRNG with live quantumness certification through the Bell test. By employing spontaneous parametric down-conversion (SPDC) in a polarization Sagnac interferometer, which generates entangled degenerate pair-photons in annular ring distribution with strong temporal and spatial correlations due to energy and momentum conservation, we divide the annular ring into six diametrically opposite sections, forming three robust entangled photon sources from a single laser and nonlinear crystal. The pair-photons from these three sources exhibit bias-free quantum mechanical randomness. By utilizing the coincidence counts of pair-photons from two sources, we generate raw bits, while the third source simultaneously measures the Bell’s parameter without any loss of QRNG bits. We have generated 90 million raw bits in 46.4 seconds with the Bell parameter (S > 2), with a minimum entropy extraction ratio exceeding 97%. Post-processed using a Toeplitz matrix, the DI-QRNG achieves a bit rate of 1.8 Mbps, passing all NIST 800-22 and TestU01 tests. In the absence of Bell’s parameter for a non-maximally entangled state, g (2) (0) can be the metric for quantumness measure. Free from the requirement of any physical devices such as beam-splitters, this scalable DI-QRNG scheme promises high bit-rates and trustworthy certifications essential for practical applications.
Quantum key distribution (QKD) using entangled photon sources (EPS) is a cornerstone of secure communication. Despite rapid advances in QKD, conventional protocols still employ beam splitters (BSs) for passive random basis selection. However, BSs intrinsically suffer from photon loss, imperfect splitting ratios, and polarization dependence, limiting the key rate, increasing the quantum bit error rate (QBER), and constraining scalability, particularly over long distances. By contrast, EPSs based on spontaneous parametric down-conversion (SPDC) intrinsically exhibit quantum randomness in spatial and spectral degrees of freedom, offering a natural replacement for BS-based basis selection. Here, we demonstrate a proof-of-concept QKD scheme that exploits the intrinsic spatial randomness of SPDC without employing beam splitters. The annular SPDC emission ring is divided into four spatial sections, effectively generating two independent EPSs whose photon pairs are distributed to Alice and Bob. Crucially, the measurement basis is not predetermined but is assigned after photon detection by exploiting intrinsic detector timing jitter, thereby concealing the basis information from a potential eavesdropper. This post-detection basis assignment emulates stochastic basis choice while avoiding BS-induced losses and bias. Experimentally, our scheme achieves a 6.4-fold enhancement in sifted key rate, a consistently reduced QBER, and a near-ideal encoding balance between linear and rectilinear bases. Furthermore, the need for four spatial channels can be avoided by employing wavelength demultiplexing to generate two EPSs at distinct wavelength pairs. Harnessing intrinsic spatial/spectral randomness thus enables robust, bias-free, high-rate, and low-QBER QKD, offering a scalable pathway for next-generation quantum networks.
We introduce a randomness beacon that the public can verify. It is based on a heralded spontaneous parametric down-conversion (SPDC) single-photon quantum random number generator (QRNG) along with a 50:50 non-polarizing beamsplitter. We time-tagged detection events from two spatial modes and processed them using a von Neumann debiasing step and SHA-256 entropy extraction. The resulting binary stream meets all NIST SP 800-22 statistical tests, demonstrating its strong randomness. We used epoch-based segmentation and a forward hash-chain to create a clear and repeatable beacon log. This lets users verify information using open-source cryptographic tools and online platforms.
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.
What is the most efficient way to generate random numbers deviceindependently using a photon pair source based on spontaneous parametric down conversion (SPDC)? We consider this question by comparing two implementations of a detection-loophole-free Bell test. In particular, we study in detail a scenario where a heralded single photon source (HSPS) is used to herald path-entangled states, i.e. entanglement between two spatial modes sharing a single photon and where nonlocality is revealed using photon counting preceded by small displacement operations. ar X iv :1 40 9. 80 51 v1 [ qu an tph ] 2 9 Se p 20 14 Device-independent quantum random number generator with a photon pair source 2 We start by giving a theoretical description of such a measurement. We then show how to optimize the Bell-CHSH violation through a non-perturbative calculation, taking the main experimental imperfections into account. We finally bound the amount of randomness that can be extracted and compare it to the one obtained with the conventional scenario using photon pairs entangled e.g. in polarization and analyzed through photon counting. While the former requires higher overall detection efficiencies, it is far more efficient in terms of both the entropy per experimental run and the rate of random bit generation. PACS numbers: 03.65.Ud Device-independent quantum random number generator with a photon pair source 3
We demonstrate a broadband entangled photon source based on a single-pass, type-0 phase-matched, non-collinear spontaneous parametric down-conversion (SPDC) process. By spatially multiplexing the intrinsically random transverse momentum states of biphotons emitted in an annular spatial distribution from a single-frequency-pumped, 2-mm-long periodically poled KTP crystal, we generate polarization-entangled pair photons with a spectral bandwidth of ∼130 nm centered at 810 nm. The negligible group-velocity mismatch of the co-polarized near-degenerate photons in single-pass and low birefringence of standard optical components preserves indistinguishability across the broadband emission without phase compensation, enabling high-quality polarization entanglement over the entire emission bandwidth. The source achieves a brightness of 0.57 Mpairs/s/mW and a two-photon coherence length of 6.97 μm, while exhibiting an interference visibility exceeding 95%, a Bell–CHSH parameter of 2.526 ± 0.005 that remains stable over 12 h of continuous operation and violates the Bell inequality by more than 100 standard deviations, and a state fidelity of 96.3%. The generic scheme providing the broadest bandwidth entangled biphotons at 810 nm, to our knowledge, can readily be used for other wavelengths as required for multiparty quantum networks and quantum sensing applications.