⚛️ quantum physics

Quantum random-number generator with non-demolition measurements: semi-device-independent implementation

This paper proposes a semi-device-independent quantum random-number generator that utilizes a tripartite system with quantum non-demolition measurements to simultaneously certify genuine quantum effects and generate near-maximal entropy random numbers, thereby eliminating the need for spacelike separation and enabling practical, scalable miniaturization.

Original authors: Paolo Solinas, Giovanni Chesi

Published 2026-07-30

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Paolo Solinas, Giovanni Chesi

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Magic of the Unseen Dice

Imagine you are trying to build a machine that rolls a truly fair die. In the world of classical physics, if you know exactly how hard you threw the die, the angle of the table, and the air resistance, you could predict the result every time. To get "randomness" in a normal computer, we have to rely on messy, hard-to-measure things like the timing of your keystrokes or the heat of the processor. But these aren't truly random; they are just too complicated for us to calculate.

Enter quantum mechanics, the rulebook for the very small. Here, nature has a built-in rule: some things are fundamentally unpredictable. You can't know the result of a quantum event before it happens, no matter how much you know about the setup. This is the holy grail for creating perfect random numbers, which are essential for unbreakable secret codes (cryptography) and secure communications.

However, there is a catch. How do you know your machine is actually using these magical quantum rules and not just a sneaky classical trick? Usually, scientists have to perform a "Bell test," which requires two detectors to be placed far apart from each other—so far that not even light could travel between them fast enough to cheat. This makes the devices huge, expensive, and impossible to shrink down for your phone or laptop. The big question is: Can we prove we have a quantum machine and get our random numbers without needing two giant, separated labs?

The One-Room Quantum Casino

In this paper, physicists Paolo Solinas and Giovanni Chesi propose a clever new way to build a Quantum Random-Number Generator (QRNG) that solves this problem. Instead of needing two detectors far apart, they use a single, compact system with three parts: one "actor" (a quantum system) and two "observers" (detectors). Think of it like a magic show where the magician (the quantum system) performs a trick, and two different judges watch from the same stage to verify the magic and collect the results.

The setup involves a three-level quantum system (our actor) and two detectors. The first detector, let's call it "Judge One," is there to certify that the magic is real. The second detector, "Judge Two," is the one that actually spits out the random numbers. The authors use a technique called "Quantum Non-Demolition Measurement" (QNDM). In plain English, this is like checking if a coin is spinning without stopping it or looking at which side is up. You can sense the "spin" (the quantum phase) without destroying the state, allowing the system to keep evolving.

Here is the clever part: Judge One looks for a specific signature of quantum magic called "negativity." In the quantum world, when paths interfere with each other (like waves in a pond), they can create a "quasi-probability" distribution. Sometimes, this distribution dips below zero. In our everyday world, probabilities can't be negative (you can't have a -50% chance of rain). But in this quantum simulation, if Judge One sees these negative numbers, it proves that the system is using genuine quantum superposition and not just a classical trick. If the numbers stay positive, the machine is just a fancy calculator.

Meanwhile, Judge Two is busy collecting the random outcomes. Because the system is in a quantum superposition, the path the system takes is a blur of possibilities. When Judge Two measures the system, it collapses this blur into a specific result. The authors show that by carefully tuning the system, they can make these results come out in a nearly perfect, uniform distribution. This means the random numbers generated are as unpredictable as possible, maximizing the "entropy" (a fancy word for true randomness).

The paper demonstrates this using a specific model with a three-level system and two detectors (one with two levels, one with three). Through calculations and simulations, they show that they can generate a string of random numbers that is almost perfectly uniform. In their example, they managed to get a distribution where the randomness was very close to the theoretical maximum, with a deviation of only about 9.81% from a perfectly uniform string. At the same time, the "negativity" detected by Judge One was strong enough to certify that the process was undeniably quantum.

What makes this so exciting is that it removes the need for the detectors to be far apart. Because the certification happens simultaneously with the generation within a single, compact setup, the device can be miniaturized. You could theoretically put this on a chip. The authors suggest that this "semi-device-independent" approach is a promising step toward scalable quantum technologies, allowing us to have secure, high-quality random number generators that don't require a massive laboratory to prove they work.

In short, Solinas and Chesi have designed a blueprint for a tiny, self-checking quantum machine. It doesn't just roll the dice; it proves the dice are fair and quantum-mechanical at the exact same moment, all while sitting in the palm of your hand.

Technical Summary: Quantum Random-Number Generator with Non-Demolition Measurements

Problem Statement
Quantum random-number generators (QRNGs) offer advantages over classical generators, such as overcoming finite periodicity and vulnerability to third-party attacks. However, practical deployment requires that end-users can certify the quantum nature of the device without understanding its internal workings or the underlying physics. Traditional device-independent QRNGs rely on Bell inequality violations, which necessitate spacelike separation between detectors. This spatial requirement imposes significant constraints on technological applications and hinders device miniaturization. While alternative approaches using Leggett-Garg inequalities (LGI) allow for sequential measurements on a single system, existing implementations suffer from limited parameter flexibility and low generation rates. The challenge is to develop a QRNG that simultaneously certifies genuine quantum effects and generates high-entropy random numbers without requiring spatial separation, thereby enabling scalable and miniaturized implementations.

Methodology
The authors propose a semi-device-independent QRNG based on a tripartite quantum system consisting of a three-level system ( $S$ ) and two ancillary detectors: a two-level detector ( $D_1$ ) and a three-level detector ( $D_2$ ). The protocol utilizes a Quantum Non-Demolition Measurement (QNDM) scheme where information about observables is encoded in the phase of the detectors.

System Evolution: The system $S$ undergoes a generic unitary evolution $\hat{u}$ , coupled sequentially to $D_1$ and $D_2$ via unitary operators $\hat{U}_1$ and $\hat{U}_2$ . The coupling operators depend on observables $\hat{a}$ and $\hat{A}$ acting on $S$ , and $\hat{\lambda}$ and $\hat{m}$ acting on the detectors.
Path Interference and Certification ( $D_1$ ): The first detector, $D_1$ , is used to certify the presence of genuine quantum effects. By tracing out $D_2$ , the protocol reconstructs a quasi-probability distribution (QPDD), $P_{ND}(\Delta)$ , derived from a quasi-characteristic function $G_\lambda$ . The presence of negative regions in $P_{ND}(\Delta)$ serves as a necessary and sufficient signature of path superposition (coherent interference), certifying the quantum nature of the dynamics. This certification occurs simultaneously with generation, rather than a posteriori.
Random Number Generation ( $D_2$ ): The second detector, $D_2$ , generates random numbers. Due to the degeneracy of the observable $\hat{A}$ , distinct evolution paths map to the same detector outcome ( $\beta \in \{0, \pm 2\}$ ). The probability distribution of these outcomes, $P_\beta(\lambda)$ , depends on the coupling parameter $\lambda$ .
Optimization: The protocol discretizes the coupling parameter $\lambda$ over $[0, 2\pi)$ . By averaging over these couplings, the oscillatory interference terms in the probability distribution vanish, leaving a distribution determined by the initial state and the unitary evolution $\hat{u}$ . This allows the distribution to be optimized to approach uniformity, thereby maximizing the entropy of the generated string.

Key Contributions

Simultaneous Generation and Certification: Unlike previous schemes where certification is performed after data collection, this protocol extracts certification data from $D_1$ and random numbers from $D_2$ simultaneously during the evolution.
Removal of Spatial Constraints: The protocol does not require spacelike separation between detectors, as it relies on temporal sequences of measurements and path interference within a single system. This removes a major physical constraint of device-independent approaches.
Semi-Device-Independent Framework: The scheme operates as a source-independent QRNG. It does not require the user to trust the specific preparation of the input states or the dimensions of the system; any manipulation of inputs would alter either the quasi-distribution (affecting certification) or the output statistics.
Trade-off Quantification: The authors derive a mathematical bound relating the certifiable quantumness (quantified by the negativity of the QPDD, specifically $P_q(-1)$ ) to the extractable randomness (min-entropy). They demonstrate that while maximizing certification requires non-zero negativity, the deviation from maximal randomness can be kept small.

Results
The authors present a specific implementation using a spin-1 formalism for system $S$ , with $\hat{a} = \hat{J}_z$ and $\hat{A} = \hat{J}_z^2$ .

Certification: Numerical simulations show that by optimizing the initial state and the evolution parameter $\theta$ , the reconstructed QPDD from $D_1$ exhibits negative regions, confirming the presence of coherent superpositions.
Randomness Generation: The resulting distribution of outcomes from $D_2$ is nearly uniform. In the optimized example, the relative deviation from the maximal min-entropy (complete uniformity) is approximately 9.81% for a sufficient number of coupling values ( $L \gtrsim 30$ ).
Independence: The study highlights that the certification process (determined by the quasi-distribution) and the statistics of the generated random numbers can be tuned independently by adjusting the initial state and evolution parameters.

Significance and Claims
The paper claims to propose a novel paradigm for QRNGs that overcomes the limitations of both Bell-based (spatially separated) and LGI-based (low rate/flexibility) approaches. The primary significance lies in the ability to generate high-entropy random numbers while simultaneously certifying their quantum origin within a compact, non-spatially-separated setup. This property facilitates the miniaturization of the device and its integration into standard electronic platforms, making it a promising candidate for scalable quantum technologies. The authors assert that their protocol achieves a balance where more than 90% of the generated numbers are genuinely random while maintaining a robust certification of quantumness. Future work suggested by the authors includes introducing additional non-demolition measurements for more complex dynamics and increasing detector dimensions to further optimize randomness extraction.

The Magic of the Unseen Dice

The One-Room Quantum Casino

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