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arXiv:2405.04244 · Physical Review A

Improving semi-device-independent randomness certification by entropy accumulation

Carles Roch i Carceller, Lucas Nunes Faria, Zhenghao Liu, Nicolò Sguerso, Ulrik L. Andersen, Jonas Schou Neergaard-Nielsen, Jonatan Bohr Brask

Published Aug 4, 2025• 4 citations
arXivHTMLPDF

Abstract

Certified randomness guaranteed to be unpredictable by adversaries is central to information security. The fundamental randomness inherent in quantum physics makes certification possible from devices that are only weakly characterized, i.e., requiring little trust in their implementation. It was recently shown that the amount of certifiable randomness can be improved using the so-called entropy accumulation theorem generalized to prepare-and-measure settings. Furthermore, this approach allows a finite-size analysis which avoids assuming that all rounds are independent and identically distributed. Here, we demonstrate this improvement in semi-device-independent randomness certification from untrusted measurements.

DOI
10.1103/dwdv-89bj

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Certified randomness guaranteed to be unpredictable by adversaries is central to information security. The fundamental randomness inherent in quantum physics makes certification possible from devices that are only weakly characterized, i.e., requiring little trust in their implementation. It was recently shown that the amount of certifiable randomness can be improved using the so-called entropy accumulation theorem generalized to prepare-and-measure settings. Furthermore, this approach allows a finite-size analysis which avoids assuming that all rounds are independent and identically distributed. Here, we demonstrate this improvement in semi-device-independent randomness certification from untrusted measurements.
Quantum measurements under realistic conditions reveal only partial information about a system. Yet, by performing sequential measurements on the same system, additional information can be accessed. We investigate this problem in the context of semi-device-independent randomness certification using sequential maximum-confidence measurements. We develop a general framework and versatile numerical methods to bound the amount of certifiable randomness in such scenarios. We further introduce a technique to compute min-tradeoff functions via semidefinite programming duality, thus making the framework suitable for bounding the certifiable randomness against adaptive attacking strategies through entropy accumulation. Our results establish sufficient criteria showing that maximum-confidence measurements enable the distribution and certification of randomness across a sequential measurement chain in single-party systems.
One of the striking properties of quantum mechanics is the occurrence of the Bell-type non-locality. They are a fundamental feature of the theory that allows two parties that share an entangled quantum system to observe correlations stronger than possible in classical physics. In addition to their theoretical significance, non-local correlations have practical applications, such as device-independent randomness generation, providing private unpredictable numbers even when obtained using devices delivered by an untrusted vendor. Thus, determining the quantity of certifiable randomness that can be produced using a specific set of non-local correlations is of significant interest. First, we present an experimental realization of recent Bell-type operators designed to provide private random numbers that are secure against adversaries with quantum resources. We use semi-definite programming to give lower bounds on the generated randomness in terms of both min-entropy and von Neumann entropy in a device-independent scenario. Our results demonstrate the first experiment that certifies nearly two bits of randomness from binary measurements of two parties [1], [2]. Apart from single-round certification, we provide an analysis of finite-key protocol for quantum randomness expansion using the Entropy Accumulation Theorem. Second, we present an efficient and practical method for certifying quantum randomness using generalized measurements. Indeed, we have derived a method for self-testing the presence of POVMs. We present the certification of more than one bit of min-entropy from a single POVM on one of the qubits of an entangled state using a variant of the elegant Bell inequality. We also obtain more than one bit of randomness in a prepare and measure scenario of a similar structure with a POVM on a single qubit [3]. We provide numerical simulations to demonstrate the effectiveness of our randomness certification and expansion.
Quantum mechanics has greatly impacted our understanding of microscopic nature. One of the key concepts of this theory is generalized measurements, which have proven useful in various quantum information processing tasks. However, despite their significance, they have not yet been shown empirically to provide an advantage in quantum randomness certification and expansion protocols. This investigation explores scenarios where generalized measurements can yield more than 1 bit of certified randomness with a single-qubit system measurement on untrusted devices and against a quantum adversary. We compare the robustness of several protocols to exhibit the advantage of exploiting generalized measurements. In our analysis of experimental data, we were able to obtain 1.21 bits of min-entropy from a measurement taken on one qubit of an entangled state. We also obtained 1.07 bits of min-entropy from an experiment with quantum state preparation and generalized measurement on a single qubit. We also provide finite data analysis for a protocol using generalized measurements and the Entropy Accumulation Theorem. Our exploration demonstrates the potential of generalized measurements to improve the certification of quantum sources of randomness and enhance the security of quantum cryptographic protocols and other areas of quantum information. Published by the American Physical Society 2024
To generate genuine random numbers, random number generators based on quantum theory are essential. However, ensuring that the process used to produce randomness meets desired security standards can pose challenges for traditional quantum random number generators. This thesis delves into Device Independent (DI) and Semi-Device Independent (semi-DI) protocols of randomness expansion, based on a minimal set of experimentally verifiable security assumptions. The security in DI protocols relies on the violation of Bell inequalities, which certify the quantum behavior of devices. The semi-DI protocols discussed in this thesis require the characterization of only one device - a power meter. These protocols exploit the fact that quantum states can be prepared such that they cannot be distinguished with certainty, thereby creating a randomness resource. In this study, we introduce enhanced DI and semi-DI protocols that surpass existing ones in terms of output randomness rate, security, or in some instances, both. Our analysis employs the Entropy Accumulation Theorem (EAT) to determine the extractable randomness for finite rounds. A notable contribution is the introduction of randomness expansion protocols that recycle input randomness, significantly enhancing finite round randomness rates for DI protocols based on the CHSH inequality violation. In the final section of the thesis, we delve into Generalized Probability Theories (GPTs), with a focus on Boxworld, the largest GPT capable of producing correlations consistent with relativity. A tractable criterion for identifying a Boxworld channel is presented.
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.
Abstract One of the striking properties of quantum mechanics is the occurrence of the Bell-type non-locality. They are a fundamental feature of the theory that allows two parties that share an entangled quantum system to observe correlations stronger than possible in classical physics. In addition to their theoretical significance, non-local correlations have practical applications, such as device-independent randomness generation, providing private unpredictable numbers even when they are obtained using devices delivered by an untrusted vendor. Thus, determining the quantity of certifiable randomness that can be produced using a specific set of non-local correlations is of significant interest. In this paper, we present an experimental realization of recent Bell-type operators designed to provide private random numbers that are secure against adversaries with quantum resources. We use semi-definite programming to provide lower bounds on the generated randomness in terms of both min-entropy and von Neumann entropy in a device-independent scenario. We compare experimental setups providing Bell violations close to the Tsirelson’s bound with lower rates of events, with setups having slightly worse levels of violation but higher event rates. Our results demonstrate the first experiment that certifies close to two bits of randomness from binary measurements of two parties. Apart from single-round certification, we provide an analysis of finite-key protocol for quantum randomness expansion using the Entropy Accumulation theorem and show its advantages compared to existing solutions.