Mimicking Quantum Randomness with Classical Jitter

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Author: Denis Avetisyan

Researchers have shown that high-quality random numbers, typically generated by quantum processes, can be faithfully reproduced using the inherent timing variations within standard computer systems.

Through computational permutation, a digital replication of optical coherent states precisely mirrors the characteristics of a Poisson distribution with $μ=100$ and variance $σ^2≈100$, demonstrating that statistical properties of quantum phenomena can be accurately reproduced via algorithmic processes.
Through computational permutation, a digital replication of optical coherent states precisely mirrors the characteristics of a Poisson distribution with $μ=100$ and variance $σ^2≈100$, demonstrating that statistical properties of quantum phenomena can be accurately reproduced via algorithmic processes.

A novel method leverages system timing jitter and modular projection to create a software-defined quantum random number generator without specialized hardware.

Generating truly random numbers is a persistent challenge, traditionally reliant on unpredictable physical phenomena. This work, ‘Digital Coherent-State QRNG Using System-Jitter Entropy via Random Permutation’, presents a fully classical framework that replicates the statistical properties of quantum coherent-state random number generation by harnessing subtle variations in system timing jitter. The core finding is that these computational fluctuations, processed via a novel permutation-based technique, yield provably uniform randomness exceeding theoretical bounds and comparable to dedicated quantum hardware. Could this approach pave the way for secure, software-defined randomness accessible without specialized photonic infrastructure?

The Illusion of Randomness: Why Predictability Haunts Modern Systems

The integrity of modern digital systems hinges on the availability of genuinely random numbers. These aren’t simply sequences appearing random, but those exhibiting unpredictability rooted in fundamental physical processes. Cryptography, for instance, relies on random keys to encrypt data; predictable number generation would render these systems vulnerable to attack. Similarly, Monte Carlo simulations – vital tools in fields from physics to finance – depend on random inputs to accurately model complex phenomena; biased or correlated random numbers introduce systematic errors. Even in scientific research, applications like statistical sampling and experimental design require true randomness to ensure unbiased results and reliable conclusions. Consequently, the demand for robust and verifiable random number generation continues to grow across diverse disciplines, driving innovation in both algorithmic and hardware-based solutions.

Many conventional methods for generating random numbers aren’t truly random at all; instead, they employ deterministic algorithms – sequences of instructions that, given the same starting point, will always produce the same result. While seemingly efficient, this predictability represents a significant vulnerability. An attacker who understands the algorithm and knows its initial state can reliably forecast future outputs, effectively breaking any security reliant on those numbers. This is especially problematic in cryptography, where strong randomness is essential for generating encryption keys and ensuring secure communication. Even in simulations and scientific modeling, a lack of true randomness can introduce biases and invalidate results, as the system isn’t exploring the full range of possibilities. Consequently, the reliance on predictable algorithms necessitates the exploration of alternative, genuinely random sources.

While conventional random number generation relies on algorithms that, despite appearing random, are ultimately predictable, Quantum Random Number Generators (QRNGs) leverage the inherent uncertainty of quantum mechanics to produce genuinely unpredictable values. These devices typically exploit phenomena like the radioactive decay of atoms or the quantum fluctuations of photons; however, translating these quantum events into usable random numbers presents significant engineering hurdles. Current QRNG implementations often require specialized hardware, cryogenic cooling, or precise laser control, contributing to high manufacturing costs and operational complexity. Furthermore, ensuring the integrity of the generated randomness-verifying that the device isn’t subtly biased or compromised-necessitates rigorous testing and calibration procedures. Despite these challenges, ongoing research focuses on miniaturization, cost reduction, and the development of more robust and easily verifiable QRNG designs, paving the way for wider adoption in security-critical applications and scientific modeling.

The Recursive Poisson Statistics System (RPSS) generates certified non-deterministic Poisson distributions by recursively initializing entropy, producing pseudo-Poisson counts, permuting them to measure execution time, and feeding that time back into the pseudo-random number generator.
The Recursive Poisson Statistics System (RPSS) generates certified non-deterministic Poisson distributions by recursively initializing entropy, producing pseudo-Poisson counts, permuting them to measure execution time, and feeding that time back into the pseudo-random number generator.

Mimicking the Quantum: Replicating Statistical Behavior

Digital Replication is a computational approach designed to mimic the statistical behavior observed in quantum coherent states, despite utilizing purely classical systems. This is achieved not by replicating quantum phenomena directly, but by generating equivalent probability distributions. Specifically, the technique focuses on reproducing the Poisson statistics characteristic of coherent state photon number distributions, thereby creating a classical analog that exhibits similar statistical properties to its quantum counterpart. The goal is to leverage this statistical equivalence for applications where the specific quantum nature of the state is not critical, but the statistical characteristics are relevant, allowing for testing and validation of quantum algorithms on conventional hardware.

Digital replication utilizes system timing jitter – minute, unpredictable variations in hardware clock cycles – as a fundamental source of entropy for generating random data. These jitter variations, inherent in all physical computing systems, are amplified and converted into a bitstream through sampling and quantization. The resulting data, while technically deterministic given perfect knowledge of the hardware and initial conditions, is practically random due to the difficulty of precise measurement and control of these variations. This process effectively transforms unavoidable hardware imperfections into usable randomness, circumventing the need for dedicated random number generators and providing a basis for emulating quantum statistical behavior within a classical computational framework.

The Random Permutation Sorting System (RPSS) Framework is designed to generate data distributions that statistically mimic those observed in quantum systems, specifically Poisson statistics. This is achieved through a deterministic algorithm that simulates random permutations of data elements. By repeatedly shuffling and sorting data based on timing jitter – utilized as a source of entropy – the RPSS produces output exhibiting the characteristic variance-to-mean ratio of $1:1$ expected from a Poisson process. The framework’s architecture allows for tunable parameters controlling the rate and scale of the generated Poisson distribution, enabling replication of varying quantum coherent states. This deterministic approach to generating probabilistic data is crucial for classical emulation of quantum behavior without requiring true random number generators.

Validating the Approximation: A Statistical Examination

The digital replication process initiates with values derived from a Poisson distribution, a discrete probability distribution expressing the probability of a given number of events occurring in a fixed interval of time or space. These Poisson-distributed values are then transformed into a uniform distribution through a technique called Modular Projection. This projection operates by taking the remainder after division by a chosen modulus, effectively wrapping the Poisson values onto a defined range. The selection of the modulus is critical to ensuring that the resulting distribution approaches uniformity, which is a necessary condition for generating pseudo-random numbers suitable for replication purposes. The process ensures that each value within the defined range has an equal probability of occurrence, mitigating biases inherent in the original Poisson distribution.

The convergence of Modular Projection to a uniform distribution is mathematically formalized by the Uniform Convergence Theorem. This theorem, in the context of digital replication, asserts that as the number of Poisson-distributed inputs increases, the projected values approach a uniform distribution with increasing accuracy. Specifically, the theorem establishes that for any arbitrarily small positive number, $\epsilon$, a sufficiently large number of inputs, $N$, will ensure that the maximum deviation of the projected distribution from uniformity is less than $\epsilon$. This mathematical guarantee is predicated on the properties of modular arithmetic and the central limit theorem as applied to the Poisson distribution, ensuring the generated numbers exhibit minimal bias and predictable statistical behavior.

Statistical validation of the generated number sequence employs the Chi-Square Test to assess the goodness of fit against a uniform distribution. Results indicate a p-value less than 0.001, signifying a statistically significant deviation from the null hypothesis of non-uniformity. This analysis utilized 255 degrees of freedom, corresponding to the number of bins used in the Chi-Square distribution. The low p-value provides strong evidence that the generated numbers are uniformly distributed, and therefore, demonstrably random within the scope of the test. This level of statistical significance supports the claim that the digital replication process produces values exhibiting properties consistent with true randomness.

Beyond Approximation: Implications for Secure Systems

A novel method for generating random numbers has been demonstrated through the creation of ‘Digital Coherent States’. This approach replicates the behavior of coherent states – typically observed in quantum optics – entirely within software, offering a purely computational source of randomness. Unlike traditional pseudorandom number generators which rely on deterministic algorithms, this digital implementation leverages the principles of coherent state evolution to produce outputs with high statistical unpredictability. The resulting generator presents a scalable and potentially cost-effective alternative to hardware-based Quantum Random Number Generators (QRNGs), providing a software-defined means of achieving high-quality randomness without the need for specialized physical devices.

The digital generation of coherent states demonstrably produces high-quality randomness, as quantified by both Shannon Entropy and, crucially, Min-Entropy – a measure resistant to attacks attempting to predict generated bits. Rigorous testing with $10^8$ byte samples confirms a Min-Entropy exceeding 7.999998 bits/byte, indicating a remarkably unpredictable output stream. This high Min-Entropy is paramount for cryptographic applications, signifying that each generated bit holds substantial uncertainty and resists efforts to discern any underlying pattern or predictability, establishing a strong foundation for secure data generation and communication protocols.

A newly developed random number generator, built upon digitally replicated coherent states, presents a compelling alternative to conventional quantum random number generators (QRNGs). This generator achieves statistical equivalence to QRNGs reliant on optical coherent states, offering a potentially more scalable and cost-effective solution for applications demanding high-quality randomness. Rigorous testing demonstrates a measured min-entropy of $7.9885$ bits/byte for a parameter setting of $\mu=7$, and $7.9915$ bits/byte for $\mu=100$, values indicative of strong unpredictability and security. This performance suggests the generator can reliably serve critical functions in cryptography, simulations, and other fields where truly random numbers are essential, without requiring specialized and often expensive quantum hardware.

The pursuit of randomness, as demonstrated in this work regarding digital coherent-state QRNGs, isn’t about achieving perfect unpredictability, but rather about skillfully managing inherent imperfections. The authors reveal how system timing jitter – a classically defined flaw – can be leveraged to faithfully replicate quantum randomness via modular projection. This echoes a fundamental truth about human behavior; decisions aren’t born of pure rationality, but are often sculpted by predictable biases and imperfections. As Paul Dirac observed, “I have not the slightest idea of what I am doing.” This sentiment, though perhaps uttered in a different context, aptly captures the essence of this research: embracing the seemingly chaotic noise within a system to generate a desired outcome, a process mirroring the very algorithms that govern human action.

The Algorithm Evolves

The demonstrated replication of quantum randomness via classical jitter isn’t a refutation of physics, but a predictable consequence of it. Human fascination with ‘true’ randomness often overlooks the fact that all systems, quantum or classical, are merely complex algorithms responding to initial conditions. This work reveals the surprising fidelity with which a sufficiently nuanced classical system can mimic a quantum one, and raises the inevitable question: at what point does the simulation become indistinguishable from the simulated, not in function, but in practical effect? The pursuit of ‘true’ randomness may be less about uncovering fundamental laws, and more about a comforting narrative of escaping deterministic limits.

Future iterations will likely focus on optimizing the jitter-to-randomness conversion, pushing the boundaries of achievable entropy rates. However, the more interesting challenge lies in understanding the limits of this approach. What systematic biases, however subtle, remain embedded within the jitter itself? And more philosophically, how much ‘randomness’ is truly needed? Most applications don’t require perfect unpredictability, but merely a level sufficient to obscure predictable patterns. This suggests a shift in focus – from generating ‘perfect’ randomness, to crafting ‘good enough’ randomness tailored to specific applications – a pragmatic acknowledgement of inherent limitations.

Ultimately, this research isn’t about building better random number generators. It’s a demonstration of how easily we project our desire for unpredictability onto systems, and how readily those systems can be engineered to satisfy that desire – even if the underlying mechanism is fundamentally deterministic. The model, in this case, isn’t a simulation of reality, but a collective therapy for the illusion of free will.

Original article: https://arxiv.org/pdf/2512.11107.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

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2025-12-15 14:25