Amplifying Randomness with Quantum Measurements
From online banking to encrypted messaging, secure communications depend on sequences of random numbers. The challenge is proving that those sequences are genuinely unpredictable. Anatoly Kulikov and colleagues at ETH Zurich in Switzerland have now created a random-number generator that uses a well-known quantum experiment—called a Bell test—to “amplify” an imperfectly random input into certifiable randomness [1].
While quantum random-number generators have been developed previously, this demonstration is the first to generate and certify randomness on a single, integrated platform, without making any assumptions about the inner workings of its hardware. Built using the same type of superconducting circuits that underpin existing quantum technologies, this device design could find broad applications across quantum communications and quantum computing infrastructures.
For a communication system to be truly secure, it needs to generate strings of numbers that lack any sort of pattern or correlation that a hacker might use to predict the next number in the sequence. These random sequences are used to generate cryptographic keys that only the sender and receiver can know.
To date, there are numerous methods available for generating random numbers. These often involve observing randomly fluctuating sources: from atmospheric noise to wax blobs inside lava lamps. While these classical techniques can indeed generate highly unpredictable numbers, their randomness ultimately relies on assumptions about complex physical processes—rather than fundamental physical unpredictability.
By contrast, quantum systems are intrinsically indeterminate—you can’t predict with certainty, for example, if a particular photon will go through a polarizer or not. Thus, much of the current effort in certifiably secure communications is focused on quantum measurements.
Inevitably, however, real-world measurements of quantum systems are subject to experimental flaws—owing both to imperfect detectors and to fluctuations in the surrounding environment. Like a loaded die, these flaws introduce a bias into the random number sequence, making some numbers more likely to appear than others.
In 2012, Roger Colbeck and Renato Renner at ETH Zurich introduced a theoretical solution to the problem, named randomness amplification [2]. In this method, weakly random numbers—those having a bias—are used as inputs to a loophole-free Bell test, an experiment that demonstrates quantum correlations between entangled particles beyond what classical physics allows.
During a loophole-free Bell test, the quantum properties of two entangled particles are measured by two spatially separated detectors, whose settings are constantly varied to ensure no coordination between the particles.
With Colbeck and Renner’s approach, the detector settings are controlled by strings of weakly random numbers (0s and 1s), which could be supplied by an imperfect quantum random-number generator. As measurements are made on the two particles, two new strings are produced—one from each of the detector outputs. By the rules of quantum physics, these output strings are inherently unpredictable, so they can be combined (with some additional math) to generate a truly random string of numbers.
The advantage of this amplification scheme is that it provides a way to check the quantum origin of the randomness. To do this, the researchers compare the detector outputs and test whether they violate a Bell inequality—a mathematical benchmark that distinguishes quantum correlations from those possible in classical systems.
Although this technique is theoretically sound, randomness amplification has proven stubbornly unattainable in practice. “For more than a decade, the required experiments remained beyond reach, as the loophole-free Bell tests involved demanded both extremely high data quality and enormous data volumes,” Kulikov explains.
Kulikov’s team has now proposed a platform specifically designed to meet both of these demands simultaneously. The design consists of two nodes, each housing a cryogenically cooled transmon qubit: a superconducting circuit that acts as a two-level quantum system.
These qubits are connected by a cryogenic link that allows them to become entangled across a 30-m distance. This distance is far enough that any signals created by the chosen settings of each Bell test would never have enough time to travel between the nodes before the measurements are carried out—ruling out any coordination between their outcomes. “We also improved the hardware implementation in terms of both data acquisition rate and entanglement quality,” Kulikov says.
These improvements allowed the researchers to generate Bell test data quickly enough and with sufficiently strong correlations to meet the strict requirements of practical randomness amplification. Unlike most other schemes, this new loophole-free Bell test uses components—the transmon qubits—that are already widely used in quantum computers.
Starting from more than 5 billion imperfectly random numbers, the researchers generated over 45 million certified random numbers, whose unpredictability is guaranteed by Bell’s inequality.
By ensuring the randomness, Kulikov’s team is confident that its approach demonstrates a clear advantage over classical random-number generators. “This experiment opens a path toward cryptographic systems operating at the physical limits of security,” Kulikov says. Possible applications include practically unbreakable codes for encrypted quantum messages, along with trustworthy, publicly accessible sources of random numbers.
The results could facilitate the use of loop-free Bell tests, says Morgan Mitchell at the Institute of Photonic Sciences in Spain, who has used these tests to create publicly certifiable random numbers [3]. “Loophole-free Bell tests are still difficult, accessible only to the most advanced research labs,” he says. “But the ETH Zurich experiments show that the circuit-QED methods can make them very efficient, giving both a high data rate and strongly nonclassical correlations.” With these capabilities, the platform could serve as the engine for a broad range of future quantum technologies: from secure communications to robust infrastructures for quantum computing.
–Sam Jarman
Samuel Jarman is a science writer based in the UK.
References
- A. Kulikov et al., “Experimental randomness amplification,” Nature 653, 1033 (2026).
- R. Colbeck and R. Renner, “Free randomness can be amplified,” Nat. Phys. 8, 450 (2012).
- G. A. Kavuri et al., “Traceable random numbers from a non-local quantum advantage,” Nature 642, 916 (2025).