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Source-device-independent Ultra-fast Quantum Random Number Generation

Davide G. Marangon, Giuseppe Vallone, Paolo Villoresi

arXiv:1509.07390v1quant-ph

TL;DR

Statistical tests cannot establish that QRNG outputs are unknown to someone with side information, while device-independent certification is experimentally demanding. The paper uses a trusted measurement device with an untrusted source and bounds conditional min-entropy through the entropic uncertainty principle. It reports secure-bit generation at 1.7 Gbit/s and a roughly 8.71 Gbit/s rate for a specified sampling and resolution setting.

  • Problem

    A posteriori statistical tests do not establish that outputs are unknown to an adversary with side information, and device-independent entropy certification requires demanding loophole-free Bell tests.

    Source: p. 1

  • Method

    The source-device-independent protocol trusts the measurement device but not the source, and uses the entropic uncertainty principle to bound conditional quantum min-entropy without assuming the source dimension.

    Source: p. 1

  • Results

    The experiment generated secure bits at 1.7 Gbit/s; at 2 GS/s and 8-bit resolution, the generator could provide a quantum-secure rate of roughly 8.71 Gbit/s.

    Source: p. 4, RATES · p. 10

  • Takeaways & Limitations

    The experiment demonstrates ultra-fast true-random-number generation with a source-device-independent protocol.

    Source: p. 4

    The protocol assumes a trusted measurement device, and classical hardware noise cannot be separated from quantum noise and affects output security.

    Source: p. 3

Abstract

from arXiv · show

Secure random numbers are a fundamental element of many applications in science, statistics, cryptography and more in general in security protocols. We present a method that enables the generation of high-speed unpredictable random numbers from the quadratures of an electromag- netic field without any assumption on the input state. The method allows to eliminate the numbers that can be predict due the presence of classical and quantum side information. In particular, we introduce a procedure to estimate a bound on the conditional min-entropy based on the Entropic Uncertainty Principle for position and momentum observables of infinite dimensional quantum sys- tems. By the above method, we experimentally demonstrated the generation of secure true random bits at a rate greater than 1 Gbit/s.

DISCRETIZATION IN CV-QRNG

Finite-resolution momentum measurements produce the raw outcomes, while measurements of the conjugate position quadrature support a lower bound on randomness secure against quantum side information. The classical min-entropy can overstate extractable randomness when the input is mixed.

DISCRETIZATION IN CV-QRNG

  • Finite-resolution quadrature measurements assign outcomes to bins of width δp; the finite measurement range contributes an estimated min-entropy error of order 10^-26.For the cited experimental data, Mδ ≈ 10.5σ and the estimate used N ≈ 25 · 10^3 measurements.Source: DISCRETIZATION IN CV-QRNG · p. 6
  • A thermal input can share the squeezed vacuum’s momentum distribution yet have lower conditional min-entropy because Eve may hold correlated quantum side information.The conjugate Q distribution can reveal the thermal state’s impurity; the classical min-entropy alone therefore does not capture its true randomness.Source: DISCRETIZATION IN CV-QRNG · p. 7, Figure S1 · p. 7
  • Measuring the conjugate Q quadrature estimates Hmax(Qδq), yielding a conservative lower bound on Hmin(Pδp|E) through the entropic uncertainty relation.This allows Alice to calibrate a randomness extractor to the conditional min-entropy without aborting when the input is mixed.Source: DISCRETIZATION IN CV-QRNG · p. 7
  • Using classical min-entropy as the security estimator can leave quantum side information held by Eve unaccounted for.For a thermal state, increasing squeezing can raise classical min-entropy while lowering the conditional min-entropy bound as Eve’s information increases.Source: DISCRETIZATION IN CV-QRNG · pp. 7–8

EXPERIMENTAL SETUP

The QRNG uses fiber-coupled commercial components and digitally filters and downsamples the detected quadrature signal. Technical noise remains in the signal and affects its security.

EXPERIMENTAL SETUP

  • The fiber-coupled setup uses a local oscillator, variable attenuator, beamsplitters, and a balanced receiver built from commercial components.Its receiver has a nominal bandwidth of 1.6 GHz and common-mode rejection ratio above 30 dB.Source: EXPERIMENTAL SETUP · pp. 8–9, Figure S4 · p. 9
  • Digital downmixing and low-pass filtering select a 1.250 GHz flat spectral region centered at f0 = 1.055 GHz to filter technical-noise regions and enhance signal-to-noise ratio.The low-pass filter cutoff was 625 MHz.Source: EXPERIMENTAL SETUP · p. 9, Figure S5 · p. 9
  • Downsampling to 1.25 GSamples/s removes oversampling correlations; residual correlation averages two orders of magnitude lower than before downsampling.Before downsampling, the autocorrelation has the sinc modulation imposed by the low-pass filter.Source: EXPERIMENTAL SETUP · p. 9, Figure S6 · p. 10
  • A nonzero variance-fit intercept, a = 2.579·10^-5 V^2, indicates non-quantum experimental noise that remains in the raw random-number signal and affects security.The fit covered LO powers from 0.5 mW to 6.5 mW; the reported slope was m = 0.0108 V^2/W.Source: EXPERIMENTAL SETUP · p. 9

RATES

The rate estimates closely match experimental measurements and approach the asymptotic conditional-entropy value as the measurement count grows. The reported rate projection depends on sampling rate and ADC resolution, with higher precision reaching a given rate using fewer measurements.

RATES

  • The distance from the asymptotic limit falls below 5% starting at m = 2.1·10^9 measurements.The green shaded region marks this threshold.Source: RATES · p. 10
  • At a sampling rate of 2 GS/s and full resolution of 8 bits, the generator could provide a quantum-secure rate of roughly 8.71 Gbit/s.Source: RATES · p. 10
  • Experimental rates agree remarkably with expected values and tend toward the asymptotic value equal to the min conditional entropy as m increases.Source: RATES · pp. 10–11

PROTOCOL’S NOISE RESILIENCY

The protocol adjusts the extracted fraction of true random bits with the signal-to-noise ratio, reducing extraction when low LO power yields a weaker quantum signal relative to classical noise.

PROTOCOL’S NOISE RESILIENCY

RESULTS OF THE STATISTICAL TESTS

The proof-of-principle post-processing produced 8.4 · 10^8 secure bits, and the extracted numbers passed the reported NIST statistical tests. A real implementation would require a stored true-random seed for the hash matrix.

RESULTS OF THE STATISTICAL TESTS

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