On-chip semi-device-independent quantum random number generator exploiting contextuality

TL;DR

A semi-device-independent quantum random number generator (QRNG) based on the violation of a contextuality inequality, implemented by the integration of two silicon photonic chips, establishes a viable route towards general-purpose, untrusted quantum random number generators compatible with practical integrated photonic quantum networks.

Abstract

We present a semi-device-independent quantum random number generator (QRNG) based on the violation of a contextuality inequality, implemented by the integration of two silicon photonic chips. Our system combines a heralded single-photon source with a reconfigurable interferometric mesh to implement qutrit state preparation, transformations, and measurements suitable for testing a KCBS contextuality inequality. This architecture enables the generation of random numbers from the intrinsic randomness of single-photon interference in a complex optical network, while simultaneously allowing a quantitative certification of their security without requiring entanglement. We observe a contextuality violation exceeding the classical bound by more than 10σ, unambiguously confirming non-classical behavior. From this violation, we certify a conditional min-entropy per experimental round of Hmin = 0.077 +- 0.002, derived via a tailored semidefinite-programming-based security analysis. Each measurement outcome therefore contains at least 0.077 +- 0.002 bits of extractable genuine randomness, corresponding to an asymptotic generation rate of 21.7 +- 0.5 bits/s. These results establish a viable route towards general-purpose, untrusted quantum random number generators compatible with practical integrated photonic quantum networks.

Figures (4)

• Figure 1: QRNG experimental scheme. a) Photon-pair source using spontaneous four-wave-mixing (SFWM). In the inset a picture of the source PIC. b) Programmable photonic circuit to manipulate single photons and perform qutrit rotations, consisting of 72 MZIs arranged in a hexagonal lattice. Each MZI can be reconfigured to perform different transformations of the two optical modes it operates on: the BAR operation ($\Delta\varphi=\pi$), the CROSS operation ($\Delta\varphi=0$), or any other tuneable two-mode coupler operation($0<\Delta \varphi<2\pi$), to realize a tuneable coupler $\Delta\varphi=\varphi_2-\varphi_1$. c) Detectors used to perform measurements: superconductive nanowire single-photon detectors (SNSPDs) and time taggers used for the counting logic. Randomness is extracted and certified in post-processing. More information about the experimental setup can be found in the Supplementary Section I.
• Figure 2: Experimental scheme implementation. a) Full scheme for the testing of the KCBS inequality. Grey lines represent optical modes; $T_i$ refer to the transformations performed on pairs of optical modes to implement the five measurement contexts. First, the desired input state is prepared in the i) step. Then, i) is followed by one of the contexts from ii)-vi). Photons are injected into the IN mode and collected at the output through single-photon detection. A coincidental detection between any of the three detectors placed on the three optical modes defining the qutrit space and the heralding photon, determines the measurement outcome of the two observables for each of the different contexts needed for building the inequality. b) Mapping of required transformations onto the hexagonal MZI mesh. $\theta$s can be directly mapped to the $T_i$ on the left. More information can be found in the Supplementary Section II.
• Figure 3: Top. Measured outcome probabilities for quantum state tomography performed in three mutually unbiased bases: the computational basis $\{|0\rangle,|1\rangle,|2\rangle\}$, the Fourier basis $\{|f_0\rangle,|f_1\rangle,|f_2\rangle\}$, and a third mutually unbiased (MU) basis $\{|v_0\rangle,|v_1\rangle,|v_2\rangle\}$. Bars show the experimental results with statistical uncertainties, and shaded regions indicate the ideal theoretical expectations. Bottom. Reconstructed density matrix of the prepared qutrit state, showing the real and imaginary components. Uncertainties are computed assuming Poissonian statistics for the raw counts and then propagated. More information regarding quantum state tomography can be found in the Supplementary Section III.
• Figure 4: Certified quantum random number generation rate as a function of the value of the KCBS witness $\chi_{\mathrm{KCBS}}$. The solid line represents the theoretical prediction including the experimentally calibrated device imperfections, detector inefficiencies, and chip losses. The experimental point with vertical error bar certifies $0.077\pm0.002~\mathrm{bits/round}$, which leads to $R_{\text{rand}} = 21.7\pm0.5~\text{bit/s}$, in good agreement with the theoretical prediction. The dashed line shows the theoretical prediction in the ideal experimental case, i.e. with state-of-the-art SFWM sources, chip losses, and detectors.