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arXiv:2511.03686

Certified randomness amplification by dynamically probing remote random quantum states

Minzhao Liu, Pradeep Niroula, Matthew DeCross, Cameron Foreman, Wen Yu Kon, Ignatius William Primaatmaja, M. S. Allman, J. P. Campora, Akhil Isanaka, Kartik Singhal, Omar Amer, Shouvanik Chakrabarti, Kaushik Chakraborty, Samuel F. Cooper, Robert D. Delaney, Joan M. Dreiling, Brian Estey, Caroline Figgatt, Cameron Foltz, John P. Gaebler, Alex Hall, Zichang He, Craig A. Holliman, Travis S. Humble, Shih-Han Hung, Ali A. Husain, Yuwei Jin, Fatih Kaleoglu, Colin J. Kennedy, Nikhil Kotibhaskar, Nathan K. Lysne, Ivaylo S. Madjarov, Michael Mills, Alistair R. Milne, Kevin Milner, Louis Narmour, Sivaprasad Omanakuttan, Annie J. Park, Michael A. Perlin, Adam P. Reed, Chris N. Self, Matthew Steinberg, David T. Stephen, Joseph Sullivan, Alex Chernoguzov, Florian J. Curchod, Anthony Ransford, Justin G. Bohnet, Brian Neyenhuis, Michael Foss-Feig, Rob Otter, Ruslan Shaydulin

quant-phSubmitted Nov 5, 2025• Announced Nov 6, 2025• 0 citations
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Abstract

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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Certified randomness using a trapped-ion quantum processor

Minzhao Liu, Ruslan Shaydulin, Pradeep Niroula +29 more

Abstract Although quantum computers can perform a wide range of practically important tasks beyond the abilities of classical computers 1,2 , realizing this potential remains a challenge. An example is to use an untrusted remote device to generate random bits that can be certified to contain a certain amount of entropy 3 . Certified randomness has many applications but is impossible to achieve solely by classical computation. Here 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 4,5 : a client generates quantum ‘challenge’ circuits using a small randomness seed, sends them to an untrusted quantum server to execute and verifies the results of the server. We analyse 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 × 10 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 present-day quantum computers.

arXiv:2503.20498•Nature•Mar 26, 2025•34 citations

Device-Independent Randomness Amplification

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Successful realization of Bell tests has settled an 80-year-long debate, proving the existence of correlations which cannot be explained by a local realistic model. Recent experimental progress allowed to rule out any possible loopholes in these tests, and opened up the possibility of applications in cryptography envisaged more than three decades ago. A prominent example of such an application is device-independent quantum key distribution, which has recently been demonstrated. One remaining gap in all existing experiments, however, is that access to perfect randomness is assumed. To tackle this problem, the concept of randomness amplification has been introduced, allowing to generate such randomness from a weak source -- a task impossible in classical physics. In this work, we demonstrate the amplification of imperfect randomness coming from a physical source. It is achieved by building on two recent developments: The first is a theoretical protocol implementing the concept of randomness amplification within an experimentally realistic setup, which however requires a combination of the degree of Bell inequality violation (S-value) and the amount of data not attained previously. The second is experimental progress enabling the execution of a loophole-free Bell test with superconducting circuits, which offers a platform to reach the necessary combination. Our experiment marks an important step in achieving the theoretical physical limits of privacy and randomness generation.

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Abstract Realistic quantum information processing devices are inherently imperfect, leading to computational errors that require quantum error correction. Likewise, random bits generated by such devices are flawed and must be enhanced to be usable for applications such as generating cryptographic keys. This enhancement of randomness quality is achieved through a protocol known as randomness amplification 1 . Here we report on an experiment that implements such a protocol. Randomness amplification is device-independent, making no assumptions about the internal workings of the quantum devices. It requires executing a loophole-free Bell test 2–4 within a specific parameter regime that involves both a high Bell violation and a high repetition rate. The experimental demonstration is made possible by a combination of theoretical advances, which allow for protocols with an experimentally realistic parameter regime, and experimental progress that achieves this regime with superconducting circuits. Crucially, randomness amplification has been proven to be impossible by purely classical means 5 . This experiment therefore demonstrates a definitive quantum advantage—leveraging quantum technology to accomplish a task unattainable by classical information processing.

Nature•May 27, 2026•4 citations

Certified Randomness from Quantum Supremacy

Scott Aaronson, Hung, Shih-Han

We propose an application for near-term quantum devices: namely, generating cryptographically certified random bits, to use (for example) in proof-of-stake cryptocurrencies. Our protocol repurposes the existing "quantum supremacy" experiments, based on random circuit sampling, that Google and USTC have successfully carried out starting in 2019. We show that, whenever the outputs of these experiments pass the now-standard Linear Cross-Entropy Benchmark (LXEB), under plausible hardness assumptions they necessarily contain $Ω(n)$ min-entropy, where $n$ is the number of qubits. To achieve a net gain in randomness, we use a small random seed to produce pseudorandom challenge circuits. In response to the challenge circuits, the quantum computer generates output strings that, after verification, can then be fed into a randomness extractor to produce certified nearly-uniform bits -- thereby "bootstrapping" from pseudorandomness to genuine randomness. We prove our protocol sound in two senses: (i) under a hardness assumption called Long List Quantum Supremacy Verification, which we justify in the random oracle model, and (ii) unconditionally in the random oracle model against an eavesdropper who could share arbitrary entanglement with the device. (Note that our protocol's output is unpredictable even to a computationally unbounded adversary who can see the random oracle.) Currently, the central drawback of our protocol is the exponential cost of verification, which in practice will limit its implementation to at most $n\sim 60$ qubits, a regime where attacks are expensive but not impossible. Modulo that drawback, our protocol appears to be the only practical application of quantum computing that both requires a QC and is physically realizable today.

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More Than One-bit Quantum Randomness Certification and Expansion

Amélie Piveteau, Alban Seguinard, Marcus Grünfeld +4 more

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.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jun 23, 2025•0 citations

Certified Randomness in Tight Space

Andreas Fyrillas, Boris Bourdoncle, Alexandre Maïnos +13 more

Reliable randomness is a core ingredient in algorithms and applications ranging from numerical simulations to statistical sampling and cryptography. The outcomes of measurements on entangled quantum states can violate Bell inequalities, thus guaranteeing their intrinsic randomness. This constitutes the basis for certified randomness generation. However, this certification requires spacelike separated devices, making it unfit for a compact apparatus. Here we provide a general method for certified randomness generation on a small-scale application-ready device and perform an integrated photonic demonstration combining a solid-state emitter and a glass chip. In contrast to most existing certification protocols, which in the absence of spacelike separation are vulnerable to loopholes inherent to realistic devices, the protocol we implement accounts for information leakage and is thus compatible with emerging compact scalable devices. We demonstrate a two-qubit photonic device that achieves the highest standard in randomness, yet is cut out for real-world applications. The full 94.5-h-long stabilized process harnesses a bright and stable single-photon quantum-dot-based source, feeding into a reconfigurable photonic chip, with stability in the milliradian range on the implemented phases and consistent indistinguishability of the entangled photons above 93%. Using the contextuality framework, we certify private randomness generation and achieve a rate compatible with randomness expansion secure against quantum adversaries. Published by the American Physical Society 2024

arXiv:2301.03536•PRX Quantum•May 30, 2024•14 citations
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 ≈0.9\approx 0.9≈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 4,5004{,}5004,500 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.
Abstract Although quantum computers can perform a wide range of practically important tasks beyond the abilities of classical computers 1,2 , realizing this potential remains a challenge. An example is to use an untrusted remote device to generate random bits that can be certified to contain a certain amount of entropy 3 . Certified randomness has many applications but is impossible to achieve solely by classical computation. Here 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 4,5 : a client generates quantum ‘challenge’ circuits using a small randomness seed, sends them to an untrusted quantum server to execute and verifies the results of the server. We analyse 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 × 10 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 present-day quantum computers.
Successful realization of Bell tests has settled an 80-year-long debate, proving the existence of correlations which cannot be explained by a local realistic model. Recent experimental progress allowed to rule out any possible loopholes in these tests, and opened up the possibility of applications in cryptography envisaged more than three decades ago. A prominent example of such an application is device-independent quantum key distribution, which has recently been demonstrated. One remaining gap in all existing experiments, however, is that access to perfect randomness is assumed. To tackle this problem, the concept of randomness amplification has been introduced, allowing to generate such randomness from a weak source -- a task impossible in classical physics. In this work, we demonstrate the amplification of imperfect randomness coming from a physical source. It is achieved by building on two recent developments: The first is a theoretical protocol implementing the concept of randomness amplification within an experimentally realistic setup, which however requires a combination of the degree of Bell inequality violation (S-value) and the amount of data not attained previously. The second is experimental progress enabling the execution of a loophole-free Bell test with superconducting circuits, which offers a platform to reach the necessary combination. Our experiment marks an important step in achieving the theoretical physical limits of privacy and randomness generation.
Abstract Realistic quantum information processing devices are inherently imperfect, leading to computational errors that require quantum error correction. Likewise, random bits generated by such devices are flawed and must be enhanced to be usable for applications such as generating cryptographic keys. This enhancement of randomness quality is achieved through a protocol known as randomness amplification 1 . Here we report on an experiment that implements such a protocol. Randomness amplification is device-independent, making no assumptions about the internal workings of the quantum devices. It requires executing a loophole-free Bell test 2–4 within a specific parameter regime that involves both a high Bell violation and a high repetition rate. The experimental demonstration is made possible by a combination of theoretical advances, which allow for protocols with an experimentally realistic parameter regime, and experimental progress that achieves this regime with superconducting circuits. Crucially, randomness amplification has been proven to be impossible by purely classical means 5 . This experiment therefore demonstrates a definitive quantum advantage—leveraging quantum technology to accomplish a task unattainable by classical information processing.
We propose an application for near-term quantum devices: namely, generating cryptographically certified random bits, to use (for example) in proof-of-stake cryptocurrencies. Our protocol repurposes the existing "quantum supremacy" experiments, based on random circuit sampling, that Google and USTC have successfully carried out starting in 2019. We show that, whenever the outputs of these experiments pass the now-standard Linear Cross-Entropy Benchmark (LXEB), under plausible hardness assumptions they necessarily contain Ω(n)Ω(n)Ω(n) min-entropy, where nnn is the number of qubits. To achieve a net gain in randomness, we use a small random seed to produce pseudorandom challenge circuits. In response to the challenge circuits, the quantum computer generates output strings that, after verification, can then be fed into a randomness extractor to produce certified nearly-uniform bits -- thereby "bootstrapping" from pseudorandomness to genuine randomness. We prove our protocol sound in two senses: (i) under a hardness assumption called Long List Quantum Supremacy Verification, which we justify in the random oracle model, and (ii) unconditionally in the random oracle model against an eavesdropper who could share arbitrary entanglement with the device. (Note that our protocol's output is unpredictable even to a computationally unbounded adversary who can see the random oracle.) Currently, the central drawback of our protocol is the exponential cost of verification, which in practice will limit its implementation to at most n∼60n\sim 60n∼60 qubits, a regime where attacks are expensive but not impossible. Modulo that drawback, our protocol appears to be the only practical application of quantum computing that both requires a QC and is physically realizable today.
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.
Reliable randomness is a core ingredient in algorithms and applications ranging from numerical simulations to statistical sampling and cryptography. The outcomes of measurements on entangled quantum states can violate Bell inequalities, thus guaranteeing their intrinsic randomness. This constitutes the basis for certified randomness generation. However, this certification requires spacelike separated devices, making it unfit for a compact apparatus. Here we provide a general method for certified randomness generation on a small-scale application-ready device and perform an integrated photonic demonstration combining a solid-state emitter and a glass chip. In contrast to most existing certification protocols, which in the absence of spacelike separation are vulnerable to loopholes inherent to realistic devices, the protocol we implement accounts for information leakage and is thus compatible with emerging compact scalable devices. We demonstrate a two-qubit photonic device that achieves the highest standard in randomness, yet is cut out for real-world applications. The full 94.5-h-long stabilized process harnesses a bright and stable single-photon quantum-dot-based source, feeding into a reconfigurable photonic chip, with stability in the milliradian range on the implemented phases and consistent indistinguishability of the entangled photons above 93%. Using the contextuality framework, we certify private randomness generation and achieve a rate compatible with randomness expansion secure against quantum adversaries. Published by the American Physical Society 2024