A new method certifies quantum randomness generated from semiconductor spin noise without detailed modelling of its underlying dynamics. Semi-device-independent quantum randomness certification has been achieved with this approach, establishing the first such certificate for any spin-noise source. The untrusted optical source was limited by an experimentally verified mean-photon-number bound alongside a stated analogue range and per-sample clipping limit. A calibrated, noisy, coarse-grained homodyne measurement characterised the trusted receiver using a semidefinite model.

High bandwidth quantum random number generation via semiconductor materials demonstrated

Certified randomness rates exceeding 3.4 Gbit/s have been achieved using semiconductor materials, representing an improvement of over two orders of magnitude compared with previous spin-noise generators which typically operated at much lower speeds. This breakthrough overcomes limitations previously preventing practical high-bandwidth quantum random number generation from solid-state sources; Queen Mary University of London and Technische Universität Dortmund successfully certified these numbers without needing detailed modelling of the underlying physics governing the source material, a key step towards more robust security protocols. The team employed a technique called semidefinite programming with controlled truncation to ensure that generated numbers remain secure even if an adversary possesses complete quantum information about the system.

This method effectively establishes a lower bound on the entropy produced per symbol while accounting for energy contributions from the solid-state emitter itself. Utilising an (In,Ga)As quantum-dot ensemble yielded certified randomness rates ranging from 3.2 to 3.4Gbit/s; 33Mbit/s was also achieved using n-GaAs within a specifically matched detection mode. These rates do not yet demonstrate practical integration into existing cryptographic systems or sustained operation under real-world environmental conditions, however.

Certified high-rate randomness via measurement device independent certification of semiconductor noise

A programme with rigorously controlled Fock-space truncation certifies randomness that remains private against an adversary holding arbitrary quantum side information. Offline analysis yields certified entropy rates of 3.2 and 3.6 Gbit/s from a singly charged (In,Ga)As quantum-dot ensemble, alongside Mbit/s from n-GaAs in a spin-noise-matched detection mode; this exceeds the rate achieved by earlier generators by more than two orders of magnitude. Random numbers underpin modern cryptography, numerical simulation and emerging quantum technologies.

Quantum random number generators exploit the intrinsic unpredictability of quantum measurements as an alternative to algorithms whose outputs are ultimately determined by an initial seed. Observing a noisy signal alone is not sufficient for secure randomness because extractable amounts depend on which parts of the apparatus we trust, how accurately they are characterised and what information might be available to an adversary. Establishing these assumptions explicitly while retaining high generation rates needed for practical applications remains central to quantum random number generation.

Different approaches make different compromises between security and experimental complexity; fully device-independent protocols certify randomness without relying on detailed models but require loophole-free Bell tests that remain difficult at conventional optical bandwidths. Device-dependent generators can reach very high rates, yet their security relies on accurate physical descriptions of both source and measurement apparatus. Semi-device-independent protocols offer a compromise: selected properties of the apparatus are calibrated and trusted, whereas remaining components are treated adversarially under testable constraints.

For continuous-variable optical measurements, a natural constraint is the mean optical energy of the incoming signal. Spin fluctuations in semiconductors provide an attractive platform for such certified generation, though this has largely remained unexplored until now. Even at thermal equilibrium, finite electron spins within an observation volume produce stochastic fluctuations of collective spin polarisation detectable optically through small Faraday rotation imparted to a probe beam.

Spin-noise spectroscopy has become established for studying semiconductor spin dynamics without deliberate polarization; it was previously used to generate random numbers in atomic vapours. Those demonstrations relied on device-dependent descriptions and were limited by comparatively narrow bandwidths. Whether solid-state spin fluctuations can support high-rate randomness certifiable without microscopic modelling remained open. Equilibrium noise in semiconductors is subject to semi-device-independent quantum certification.

Earlier generators employed either device dependence or vacuum/coherent light; no certificate had been obtained from any kind of spin-noise source until now. A balanced homodyne receiver measures the weak optical field generated orthogonal to an incident probe beam, treating local oscillator, interferometer, detector, digitiser and binning as a calibrated measurement apparatus. No model is assigned to the semiconductor source: it may produce states correlated with arbitrary quantum side information held by an adversary provided that it satisfies tested mean photon number bounds and declared analogue range conditions.

The observed outcomes are described by this calibrated noisy coarse-grained homodyne measurement. Semidefinite programming (SDP) alongside rigorously controlled truncation of the optical Fock space bound conditional min-entropy of measurement outcomes. An important feature is that measured spin noise cannot artificially increase certified randomness; additional energy enlarges available adversarial states lowering entropy instead. Consequently, measurements test whether substantial randomness can be certified even when fluctuating solid-state signals are present and experimentally resolved.

The source-energy bound may either be supplied as an independent parameter or determined within the protocol via two quadrature measurements because a source could appear vacuum in one while carrying unrestricted energy orthogonally. This framework was applied to complementary systems: n-doped GaAs epilayer with narrow Larmor resonance yielding Mbit/s for 131ms acquisition, and singly charged (In,Ga)As quantum dot ensemble where hyperfine variations broaden fluctuations across receiver bandwidth enabling rates of 3.2 and 3.6 Gbit/s, more than two orders above existing generators. Although current analysis is offline using fixed phase records, the same framework allows real-time operation through randomised switching between test and generation rounds.

Two protocols are presented; Protocol 1 uses independently validated input whereas Protocol 2 estimates it from measurements costing one statistical confidence parameter. Throughout “certified” denotes certification relative to calibrated model assumptions detailed in Methods. Supplementary Table S3 positions this work against earlier spin-noise and continuous variable generators while security theorems proofs calibration records reside within Methods Supplementary Notes 1 Results.

In a finite ensemble oppositely oriented spins never balance exactly but fluctuate spontaneously. A polarised probe transmitted through such an ensemble experiences fluctuating magnetisation producing weak orthogonal polarisation via magneto-optical interaction. Balanced homodyne detection converts this field into rapidly varying electrical signals; conventional spectroscopy extracts dynamical parameters, however spectral distribution determines bandwidth available for randomness generation.

summarises three regimes studied experimentally: broadband GaAs detection, mode matched to narrow Larmor resonance and broadened quantum dot ensemble detection. All scenarios use the same calibrated receiver model, so differences in rates trace temporal mode selection rather than assumed correspondence between variance intrinsic randomness. The certification model divides generation into an untrusted source and a trusted receiver as illustrated.

The untrusted component is a weak optical field originating from the sample’s orthogonal polarisation channel denoted A, potentially correlated with any quantum system E controlled by an adversary represented by joint state ρAE. Microscopic modelling of the semiconductor material is not required; instead, operation obeys Try(ρAn) ≤ n where n represents the photon number operator for one detected mode and defines its mean energy upper bound.

The trusted device includes a local oscillator, interferometer, balanced detector, analogue-to-digital electronics, phase control mechanisms and classical post-processing to map calibrated output into discrete bins. Three parameters characterise response: noise variance σ2, bin width δ and boundary xmax defining interior detection range (values are in Supplementary Table S2).

Finite receiver range and saturation conditions prevent signals outside this range from being accepted as valid generation outcomes. Given the calibrated POVM and energy bound SDP searches for state making digitised outcome easiest to predict yielding certified entropy h∗ cert(n) defined by Eq. Calculation performed truncated Fock space correcting neglected higher photon number states; it remains valid against arbitrary quantum side information without identifying observed spin-noise as private entropy.

Two protocols establish bounds. Finite sample statistics corrections saturation phase calibration uncertainty local oscillator instability included resulting in a final bound of 0.3 signal LO digitised output -1 0 1 -1 0 0 -1 1 0 1.

GaAs QD ensemble A B D Bx probe probe stochastic QDs GaAs ρAE Untrusted source Trusted measurement semiconductor sample adversary GT nPBS BPRT ADC digitised symbols certified random bits quantum proof extractor Tested energy bound min entropy per symbol SDP Test rounds probe probe probe GaAs C Spin noise matched GaAs Signal resolved QD Vacuum limited GaAs Signal LO PD1 PD2 Digitised output i1(t) i2(t) i(t) i1(t) i2(t) i(t) QDs x z y δθF(t) δθF(t): Source adversarial certification semiconductor spin noise. A singly charged (,Ga)As quantum-dot ensemble and n-GaAs systems demonstrate potential for high-bandwidth quantum random-number generation, though certifying randomness requires addressing complex dynamics.

This work presents semi-device-independent certification of quantum randomness derived from semiconductor spin noise, a first such certificate applied to any spin-noise source without relying on detailed modelling of the spin system.

Researchers have demonstrated a method for certifying that random numbers generated from semiconductor spin noise are genuinely quantum in origin, achieving this without needing a precise understanding of the underlying physics. This certification allows for high data generation rates of up to 3.4Gbit/s using an (In,Ga)As quantum-dot ensemble and 33$Mbit/s with n-GaAs. The technique relies on experimentally testing limits related to the light source and employing calibrated measurement equipment; it confirms randomness even when considering potential adversaries possessing complete information about the system. Authors suggest further work may refine these bounds and improve performance.

👉 More information
🗞 Semi-device-independent quantum randomness certification in semiconductor spin-noise measurements
✍️ Hamid Tebyanian, Marius Cizauskas, Manfred Bayer, Marc Assmann and Alex Greilich
🧠 ArXiv: https://arxiv.org/abs/2609.10037

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