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arXiv:2111.06186 · Physical Review A

Steering-based randomness certification with squeezed states and homodyne measurements

Marie Ioannou, Bradley Longstaff, Mikkel V. Larsen, Jonas Schou Neergaard-Nielsen, Ulrik L. Andersen, Daniel Cavalcanti, Nicolas Brunner, Jonatan Bohr Brask

Published Oct 13, 2022• 11 citations
arXivHTMLPDF

Abstract

High-quality randomness, certified to be unpredictable by eavesdroppers, is key to secure information processing. Quantum mechanics enables randomness certification with minimal trust in the devices used, by exploiting quantum nonlocality. However, such full device independence is challenging to implement. We present a scheme for quantum randomness certification based on quantum steering. The protocol is one-sided device independent, providing high security, but requires only states and measurements that are simple to realize on quantum optics platforms---squeezed vacuum states and homodyne detection. This ease of implementation is demonstrated experimentally and implies that gigahertz random bit rates should be attainable with current technology. Furthermore, our scheme is immune to the detection loophole and represents the closest to full device independence that can be achieved using purely Gaussian states and measurements.

DOI
10.1103/physreva.106.042414

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High-quality randomness, certified to be unpredictable by eavesdroppers, is key to secure information processing. Quantum mechanics enables randomness certification with minimal trust in the devices used, by exploiting quantum nonlocality. However, such full device independence is challenging to implement. We present a scheme for quantum randomness certification based on quantum steering. The protocol is one-sided device independent, providing high security, but requires only states and measurements that are simple to realize on quantum optics platforms---squeezed vacuum states and homodyne detection. This ease of implementation is demonstrated experimentally and implies that gigahertz random bit rates should be attainable with current technology. Furthermore, our scheme is immune to the detection loophole and represents the closest to full device independence that can be achieved using purely Gaussian states and measurements.
We present a scheme for semi-device-independent quantum randomness certification from an untrusted measurement device and a trusted source and demonstrate it experimentally. No assumptions about noise or imperfections in the measurement are required and the scheme is simple to implement with existing technology. The measurement device is probed with a few trusted states and the output entropy can be lower bounded conditioned on the observed outcome distribution. The protocol can be applied to measurements with any finite number of outcomes and in particular can be realised by homodyne measurements of the vacuum using a detector probed by coherent states, as we experimentally demonstrate by intensity modulation of a telecom-wavelength pilot laser followed by homodyne detection and discretisation by analog-to-digital conversion. We show that randomness can be certified in the presence of both Gaussian additive noise and non-Gaussian imperfections.
The generation of certifiable randomness is one of the most promising applications of quantum technologies. Furthermore, the intrinsic non-locality of quantum correlations allow us to certify randomness in a device-independent way, i.e., we do not need to make assumptions about the devices used. Due to the work of Curchod et al. a single entangled two-qubit pure state can be used to produce arbitrary amounts of certified randomness. However, the obtaining of this randomness is experimentally challenging as it requires a large number of measurements, both projective and general. Motivated by these difficulties in the device-independent setting, we instead consider the scenario of one-sided device independence where certain devices are trusted, and others are not; a scenario motivated by asymmetric experimental set-ups such as ion-photon networks. We show how certain aspects of previous works can be adapted to this scenario and provide theoretical bounds on the amount of randomness that can be certified. Furthermore, we give a protocol for unbounded randomness certification in this scenario, and provide numerical results demonstrating the protocol in the ideal case. Finally, we numerically test the possibility of implementing this scheme on near-term quantum technologies, by considering the performance of the protocol on several physical platforms.
We consider quantum steering certification in multipartite networks, with a focus on minimal trust scenarios: all-except-one parties are untrusted and treated device-independently. We show that it is always possible to lift steering certification to the measurement-device-independent regime, in which even the (last) trusted party can treat their local hardware as a black-box, except for a set of fiduciary quantum states used as the inputs to the experiment. This holds both for finite-dimensional systems as well as for bosonic continuous-variable systems, which we characterize in terms of semi-quantum games in the bipartite case. Additionally, we introduce measurement-device-independent network steering protocols based entirely on Gaussian operations -- which cannot be used for fully device-independent protocols, and thus become instead a viable option for minimal trust certification as soon as a single trusted input is inserted in the network. Our results present a basis for steering-based applications (such as randomness generation) with minimal trust beyond full nonlocality and with feasible experimental requirements.
Randomness is fundamental for secure communication and information processing. While continuous-variable optical systems offer an attractive platform for this task, certifying genuine quantum randomness in such setups remains challenging. We present a semi-device-independent scheme for randomness certification tailored to continuous-variable implementations, where the dimension assumption is operationally implemented by restricting state preparations to the two-level Fock subspace. Using standard homodyne and displacement-based measurements, we show that simple optical setups can achieve dimension-witness violations that certify positive min-entropy, even in the presence of realistic losses and misaligned reference frames. These results demonstrate that practical and scalable quantum randomness generation is achievable with minimal experimental complexity on continuous-variable platforms.
The generation of certifiable randomness is one of the most promising applications of quantum technologies. Furthermore, the intrinsic non-locality of quantum correlations allow us to certify randomness in a device-independent way, ie, we do not need to make assumptions about the devices used. Due to the work of Curchod et al. a single entangled two-qubit pure state can be used to produce arbitrary amounts of certified randomness. However, the obtaining of this randomness is experimentally challenging as it requires a large number of measurements, both projective and general. Motivated by these difficulties in the device-independent setting, we instead consider the scenario of one-sided device independence where certain devices are trusted, and others are not; a scenario motivated by asymmetric experimental set-ups such as ion-photon networks. We show how certain aspects of previous works can be adapted to this scenario and provide theoretical bounds on the amount of randomness that can be certified. Furthermore, we give a protocol for unbounded randomness certification in this scenario, and provide numerical results demonstrating the protocol in the ideal case. Finally, we numerically test the possibility of implementing this scheme on near-term quantum technologies, by considering the performance of the protocol on several physical platforms.
Complex solid-state systems are promising platforms for scalable, high-bandwidth quantum random-number generation, yet certifying the quantum origin of their fluctuations remains difficult because the underlying microscopic dynamics are hard to model and validate. Here we demonstrate semi-device-independent quantum randomness certification from semiconductor spin noise, to our knowledge the first such certificate on any spin-noise source, without relying on a microscopic model of the spin system. The untrusted optical source is constrained by an experimentally tested mean-photon-number bound together with a declared analogue-range and per-sample clipping ceiling, while the trusted receiver is described as a calibrated, noisy, coarse-grained homodyne measurement. Using a semidefinite programme with rigorously controlled Fock-space truncation, we certify randomness that remains private against an adversary holding arbitrary quantum side information. Offline analysis yields certified entropy rates of 3.23.23.2--3.43.43.4\,Gbit/s from a singly charged (In,Ga)As quantum-dot ensemble and 333333\,Mbit/s from nnn-GaAs in a spin-noise-matched detection mode. This exceeds the certified entropy rate of earlier spin-noise generators by more than two orders of magnitude, and the certificate tolerates a resolved per-symbol energy contribution from the solid-state emitter itself rather than requiring a near-vacuum input.