arXiv subjects

Florian J. Curchod

Publications and source records attributed to Florian J. Curchod.

9 recordsLinked to original sources

arXiv2026

More entropy from shorter experiments using polytope approximations to the quantum set

We introduce a systematic method for constructing polytope approximations to the quantum set in a variety of device-independent quantum random number generation (DI-QRNG) protocols. Our approach relies on two general-purpose algorithms that iteratively refine an initial outer-polytope approximation, guided by typical device behaviour and cryptographic intuition. These refinements strike a balance between computational tractability and approximation effectiveness. By integrating these approximations into the probability estimation (PE) framework [Zhang et al., PRA 2018], we obtain significantly improved certified entropy bounds in the finite-size regime. We test our method on various bipartite and tripartite DI-QRNG protocols, using both simulated and experimental data. In all cases, it yields notably higher entropy rates with fewer device uses than the existing techniques. We further extend our analysis to the more demanding task of randomness amplification, demonstrating major performance gains without added complexity. These results offer an effective and ready-to-use method to prove security-with improved certified entropy rates-in the most common practical DI-QRNG protocols. Our algorithms and entropy certification with PE tools are publicly available under a non-commercial license at https://github.com/CQCL/PE_polytope_approximation.

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arXiv2025

Cryptomite: A versatile and user-friendly library of randomness extractors

We present Cryptomite, a Python library of randomness extractor implementations. The library offers a range of two-source, seeded and deterministic randomness extractors, together with parameter calculation modules, making it easy to use and suitable for a variety of applications. We also present theoretical results, including new extractor constructions and improvements to existing extractor parameters. The extractor implementations are efficient in practice and tolerate input sizes of up to $2^{40}>10^{12}$ bits. Contrary to alternatives using the fast Fourier transform, we implement convolutions efficiently using the number-theoretic transform to avoid rounding errors, making them well suited to cryptography. The algorithms and parameter calculation are described in detail, including illustrative code examples and performance benchmarking.

cs.CR↗

arXiv2025

Certified randomness amplification by dynamically probing remote random quantum states

Cryptography depends on truly unpredictable numbers, but physical sources emit biased or correlated bits. Quantum mechanics enables the amplification of imperfect randomness into nearly perfect randomness, but prior demonstrations have required physically co-located, loophole-free Bell tests, constraining the feasibility of remote operation. Here we realize certified randomness amplification across a network by dynamically probing large, entangled quantum states on Quantinuum's 98-qubit Helios trapped-ion quantum processor. Our protocol is secure even if the remote device acts maliciously or is compromised by an intercepting adversary, provided the samples are generated quickly enough to preclude classical simulation of the quantum circuits. We stream quantum gates in real time to the quantum processor, maintain quantum state coherence for $\approx 0.9$ seconds, and then reveal the measurement bases to the quantum processor only milliseconds before measurement. This limits the time for classical spoofing to 30 ms and constrains the location of hypothetical adversaries to a $4{,}500$ km radius. We achieve a fidelity of 0.586 on random circuits with 64 qubits and 276 two-qubit gates, enabling the amplification of realistic imperfect randomness with a low entropy rate into nearly perfect randomness.

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arXiv2025

An efficient construction of Raz's two-source randomness extractor with improved parameters

Randomness extractors are algorithms that distill weak random sources into near-perfect random numbers. Two-source extractors enable this distillation process by combining two independent weak random sources. Raz's extractor (STOC '05) was the first to achieve this in a setting where one source has linear min-entropy (i.e., proportional to its length), while the other has only logarithmic min-entropy in its length. However, Raz's original construction is impractical due to a polynomial computation time of at least degree 4. Our work solves this problem by presenting an improved version of Raz's extractor with quasi-linear computation time, as well as a new analytic theorem with reduced entropy requirements. We provide comprehensive analytical and numerical comparisons of our construction with others in the literature, and we derive strong and quantum-proof versions of our efficient Raz extractor. Additionally, we offer an easy-to-use, open-source code implementation of the extractor and a numerical parameter calculation module.

cs.CR↗

arXiv2025

Certified randomness using a trapped-ion quantum processor

While quantum computers have the potential to perform a wide range of practically important tasks beyond the capabilities of classical computers, realizing this potential remains a challenge. One such task is to use an untrusted remote device to generate random bits that can be certified to contain a certain amount of entropy. Certified randomness has many applications but is fundamentally impossible to achieve solely by classical computation. In this work, we demonstrate the generation of certifiably random bits using the 56-qubit Quantinuum H2-1 trapped-ion quantum computer accessed over the internet. Our protocol leverages the classical hardness of recent random circuit sampling demonstrations: a client generates quantum "challenge" circuits using a small randomness seed, sends them to an untrusted quantum server to execute, and verifies the server's results. We analyze the security of our protocol against a restricted class of realistic near-term adversaries. Using classical verification with measured combined sustained performance of $1.1\times10^{18}$ floating-point operations per second across multiple supercomputers, we certify $71,313$ bits of entropy under this restricted adversary and additional assumptions. Our results demonstrate a step towards the practical applicability of today's quantum computers.

quant-ph↗

arXiv2025

Statistical testing of random number generators and their improvement using randomness extraction

Random number generators (RNGs) are notoriously challenging to build and test, especially for cryptographic applications. While statistical tests cannot definitively guarantee an RNG's output quality, they are a powerful verification tool and the only universally applicable testing method. In this work, we design, implement, and present various post-processing methods, using randomness extractors, to improve the RNG output quality and compare them through statistical testing. We begin by performing intensive tests on three RNGs -- the 32-bit linear feedback shift register (LFSR), Intel's 'RDSEED,' and IDQuantique's 'Quantis' -- and compare their performance. Next, we apply the different post-processing methods to each RNG and conduct further intensive testing on the processed output. To facilitate this, we introduce a comprehensive statistical testing environment, based on existing test suites, that can be parametrised for lightweight (fast) to intensive testing.

cs.CR↗

arXiv2023

Practical randomness amplification and privatisation with implementations on quantum computers

We present an end-to-end and practical randomness amplification and privatisation protocol based on Bell tests. This allows the building of device-independent random number generators which output (near-)perfectly unbiased and private numbers, even if using an uncharacterised quantum device potentially built by an adversary. Our generation rates are linear in the repetition rate of the quantum device and the classical randomness post-processing has quasi-linear complexity - making it efficient on a standard personal laptop. The statistical analysis is also tailored for real-world quantum devices. Our protocol is then showcased on several different quantum computers. Although not purposely built for the task, we show that quantum computers can run faithful Bell tests by adding minimal assumptions. In this semi-device-independent manner, our protocol generates (near-)perfectly unbiased and private random numbers on today's quantum computers.

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arXiv2018

A versatile construction of Bell inequalities for the multipartite scenario

Local measurements acting on entangled quantum states give rise to a rich correlation structure in the multipartite scenario. We introduce a versatile technique to build families of Bell inequalities witnessing different notions of multipartite nonlocality for any number of parties. The idea behind our method is simple: a known Bell inequality satisfying certain constraints, for example the Clauser-Horne-Shimony-Holt inequality, serves as the $seed$ to build new families of inequalities for more parties. The constructed inequalities have a clear operational meaning, capturing an essential feature of multipartite correlations: their violation implies that numerous subgroups of parties violate the inequality chosen as seed. The more multipartite nonlocal the correlations, the more subgroups can violate the seed. We illustrate our construction using different seeds and designing Bell inequalities to detect $m$-way nonlocal multipartite correlations, in particular, $genuine$ $multipartite$ $nonlocal$ correlations -- the strongest notion of multipartite nonlocality. For one of our inequalities we prove analytically that a large class of pure states that are genuine multipartite entangled exhibit genuine multipartite nonlocality for any number of parties, even for some states that are almost product. We also provide numerical evidence that this family is violated by all genuine multipartite entangled pure states of three and four qubits. Our results make us conjecture that this family of Bell inequalities can be used to prove the equivalence between genuine multipartite pure-state entanglement and nonlocality for any number of parties.

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arXiv2018

Entangled systems are unbounded sources of nonlocal correlations and of certified random numbers

The outcomes of local measurements made on entangled systems can be certified to be random provided that the generated statistics violate a Bell inequality. This way of producing randomness relies only on a minimal set of assumptions because it is independent of the internal functioning of the devices generating the random outcomes. In this context it is crucial to understand both qualitatively and quantitatively how the three fundamental quantities -- entanglement, non-locality and randomness -- relate to each other. To explore these relationships, we consider the case where repeated (non projective) measurements are made on the physical systems, each measurement being made on the post-measurement state of the previous measurement. In this work, we focus on the following questions: For systems in a given entangled state, how many nonlocal correlations in a sequence can we obtain by measuring them repeatedly? And from this generated sequence of non-local correlations, how many random numbers is it possible to certify? In the standard scenario with a single measurement in the sequence, it is possible to generate non-local correlations between two distant observers only and the amount of random numbers is very limited. Here we show that we can overcome these limitations and obtain any amount of certified random numbers from an entangled pair of qubit in a pure state by making sequences of measurements on it. Moreover, the state can be arbitrarily weakly entangled. In addition, this certification is achieved by near-maximal violation of a particular Bell inequality for each measurement in the sequence. We also present numerical results giving insight on the resistance to imperfections and on the importance of the strength of the measurements in our scheme.

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