Vacuum fluctuations Secure heterodyne-based quantum random number quantum random number generator with non-iid generator at 17 Gbps samples Tobias Gehring et al. Marco Avesani et al. 1
The need for random numbers Alice quantum Rx laser channel DSP IQmod Tx laser VATT 50/50 splitter Bob Random Modulation Poster 49 2
The need for random numbers Alice quantum Rx laser channel DSP IQmod Tx laser VATT 50/50 splitter Bob Random Modulation Poster 49 Certified Security 3
The need for random numbers Alice quantum Rx laser channel DSP IQmod Tx laser VATT 50/50 splitter Bob Random Modulation Poster 49 Unpredictable / Certified Private Security 4
The need for random numbers Alice quantum Rx laser channel DSP IQmod Tx laser VATT 50/50 splitter Bob Random Modulation Poster 49 Fast real-time generation Unpredictable / Certified Private Security 5
The need for random numbers Alice quantum Rx laser channel DSP IQmod Tx laser VATT 50/50 splitter Bob Random Modulation Poster 49 Many other applications: Fast real-time ● Simulations generation ● Gambling Unpredictable / Certified Private ● Classical Key Generation Security ● etc 6
Randomness Certification How can one guarantee that the random numbers are truly random? 7
Randomness Certification How can one guarantee that the random numbers are truly random? Source Detector Device-Independent 8
Randomness Certification How can one guarantee that the random numbers are truly random? Source Detector Device-Independent More assumptions 9
Randomness Certification How can one guarantee that the random numbers are truly random? Source Source Detector Device-Independent Source-Independent More assumptions 10
Randomness Certification How can one guarantee that the random numbers are truly random? Source Source Detector Device-Independent Source-Independent Device Dependent More assumptions 11
Vacuum fluctuations quantum random number generator with non-iid samples Tobias Gehring 1 , Arne Kordts 1 , Dino Solar Nikolic 1 , Nitin Jain 1 , Cosmo Lupo 2 , Stefano Pirandola 2 , Thomas B. Pedersen 3 , Ulrik L. Andersen 1 1) Department of Physics, Technical University of Denmark, Denmark 2) Department of Computer Science, University of York, UK 3) Cryptomathic A/S, Denmark
Experimental Setup Transimpedance PD Bending Amplifier Amplifier Loss FPGA Laser Coupler Toeplitz Output ADC Fifo Extractor Fifo Lowpass 1 GS/s 10.67 GBit/s PD 16 bit Vacuum fluctuations quantum random number generator with non-iid samples 13
Experimental Setup Transimpedance PD Bending Amplifier Amplifier Loss FPGA Laser Coupler Toeplitz Output ADC Fifo Extractor Fifo Lowpass 1 GS/s 10.67 GBit/s PD 16 bit Vacuum fluctuations quantum random number generator with non-iid samples 14
Experimental Setup Transimpedance PD Bending Amplifier Amplifier Loss FPGA Laser Coupler Toeplitz Output ADC Fifo Extractor Fifo Lowpass 1 GS/s 10.67 GBit/s PD 16 bit Vacuum fluctuations quantum random number generator with non-iid samples 15
Correlated Samples 0 1.0 Norm. Power Spectral 0.1 0.8 Autocorrelation Density [dB/Hz] -10 0.6 0 -20 0.4 -30 0.2 -0.1 0 5 10 0.0 -40 0 5 10 15 20 25 10 6 10 7 10 8 Frequency [Hz] Delay [ns] Vacuum fluctuations quantum random number generator with non-iid samples 16
Correlated Samples 0 1.0 Norm. Power Spectral 0.1 0.8 Autocorrelation Density [dB/Hz] -10 0.6 0 -20 0.4 -30 0.2 -0.1 0 5 10 0.0 -40 0 5 10 15 20 25 10 6 10 7 10 8 Frequency [Hz] Delay [ns] Samples are not independently distributed! Vacuum fluctuations quantum random number generator with non-iid samples 17
Correlated Samples 0 1.0 Norm. Power Spectral 0.1 0.8 Autocorrelation Density [dB/Hz] -10 0.6 0 -20 0.4 -30 0.2 -0.1 0 5 10 0.0 -40 0 5 10 15 20 25 10 6 10 7 10 8 Frequency [Hz] Delay [ns] Samples are not independently distributed! Idea: Map non-i.i.d. into i.i.d. process Vacuum fluctuations quantum random number generator with non-iid samples 18
Correlated Samples 0 1.0 Norm. Power Spectral 0.1 0.8 Autocorrelation Density [dB/Hz] -10 0.6 0 -20 0.4 -30 0.2 -0.1 0 5 10 0.0 -40 0 5 10 15 20 25 10 6 10 7 10 8 Frequency [Hz] Delay [ns] Samples are not independently distributed! Idea: Map non-i.i.d. into i.i.d. process Conditional variance describes variance of virtual i.i.d. process Power spectral density of the signal Vacuum fluctuations quantum random number generator with non-iid samples 19
Metrological characterization ● Min-Entropy model has three parameters: Vacuum fluctuations quantum random number generator with non-iid samples 20
Metrological characterization ● Min-Entropy model has three parameters: ● Variance of the signal Vacuum fluctuations quantum random number generator with non-iid samples 21
Metrological characterization ● Min-Entropy model has three parameters: ● Variance of the signal ● Conditional variance of the signal Vacuum fluctuations quantum random number generator with non-iid samples 22
Metrological characterization ● Min-Entropy model has three parameters: ● Variance of the signal ● Conditional variance of the signal ● Conditional variance of the excess noise Vacuum fluctuations quantum random number generator with non-iid samples 23
Metrological characterization ● Min-Entropy model has three parameters: ● Variance of the signal ● Conditional variance of the signal ● Conditional variance of the excess noise ● Characterize all of them with confidence intervals Vacuum fluctuations quantum random number generator with non-iid samples 24
Metrological characterization ● Min-Entropy model has three parameters: ● Variance of the signal ● Conditional variance of the signal ● Conditional variance of the excess noise ● Characterize all of them with confidence intervals ● Take the minimum min-entropy which is compatible with the confidence intervals Vacuum fluctuations quantum random number generator with non-iid samples 25
Metrological characterization ● Min-Entropy model has three parameters: } ● Variance of the signal “Simple” ● Conditional variance of the signal ● Conditional variance of the excess noise ● Characterize all of them with confidence intervals ● Take the minimum min-entropy which is compatible with the confidence intervals Vacuum fluctuations quantum random number generator with non-iid samples 26
Metrological characterization ● Min-Entropy model has three parameters: } ● Variance of the signal “Simple” ● Conditional variance of the signal ● Conditional variance of the excess noise } “Hard” ● Characterize all of them with confidence intervals ● Take the minimum min-entropy which is compatible with the confidence intervals Vacuum fluctuations quantum random number generator with non-iid samples 27
Metrological-Grade Characterization Power Spectral Density [dB/Hz] Signal -10 Excess Noise -15 Vacuum -20 Fluctuations -25 -30 10 6 10 7 10 8 Frequency [Hz] Vacuum fluctuations quantum random number generator with non-iid samples 28
Metrological-Grade Characterization Power Spectral Density [dB/Hz] Signal -10 Vacuum fluctuations given Excess Noise by Schottky shot noise -15 Vacuum -20 Fluctuations -25 -30 10 6 10 7 10 8 Frequency [Hz] Vacuum fluctuations quantum random number generator with non-iid samples 29
Metrological-Grade Characterization Power Spectral Density [dB/Hz] Signal -10 Vacuum fluctuations given Excess Noise by Schottky shot noise -15 Vacuum -20 Fluctuations -25 -30 10 6 10 7 10 8 Frequency [Hz] Bending Power Transimpedance 1% PD Loss Meter Amplifier Amplifier FPGA 99% Coupler DDR4 RAM VATT Signal 20 dB ADC Laser Lowpass Attenuator Laser PD (Local Oscillator) Vacuum fluctuations quantum random number generator with non-iid samples 30
Metrological-Grade Characterization Power Spectral Density [dB/Hz] Signal -10 Vacuum fluctuations given Excess Noise by Schottky shot noise -15 Vacuum -20 Fluctuations -25 Lower bound as ● Visibility = 1 -30 ● Quantum efficiency = 1 10 6 10 7 10 8 Frequency [Hz] Bending Power Transimpedance 1% PD Loss Meter Amplifier Amplifier FPGA 99% Coupler DDR4 RAM VATT Signal 20 dB ADC Laser Lowpass Attenuator Laser PD (Local Oscillator) Vacuum fluctuations quantum random number generator with non-iid samples 31
Summary Real-time QRNG suitable for high speed QKD ● Min-Entropy: 11.4 bit per 16 bit sample ● Real-time randomness extraction: 10.67 Gbit/s ● Metrological characterization: QRNG runs in the past Outlook ● Where to get good seed bits from? DI-QRNG? ● Integration into a package suitable for QKD integration ● Online tests ● Power-on self-tests Vacuum fluctuations quantum random number generator with non-iid samples 32
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