Laboratories are already creating quantum states in which millions of atoms behave as a single whole, contrary to all the expectations of classical physics. New measures of "extensive size" and "entangled size" make it possible to precisely assess the scale of this coherence and entanglement in real experiments with mechanical systems.
The theorists Benjamin Yadin of the University of Siegen in Germany and Matteo Fadel of Peking University and ETH Zürich published a paper on 30 October 2026 in the journal Quantum in which they introduce two independent measures. The first — extensive size — shows over what distance or momentum coherence is preserved relative to atomic scales. The second — entangled size — counts the minimum number of subsystems that must be entangled in order to explain the observed data. Both measures rest on rigorous concepts of quantum information theory and are applicable to experimental results.
The authors applied the measures to recent experiments with micromechanical oscillators and molecular diffraction. As a result, they obtained lower bounds on genuine multipartite entanglement — true many-particle entanglement — at the level of from 10^5 to 10^7 atoms. This means that to explain the observed interference patterns, exactly that many particles must be considered entangled, and no fewer.
Imagine an ordinary string of lights: if one bulb goes out, the whole chain may go dark. Here, by contrast, entanglement links atoms in such a way that the behavior of the entire system depends on the collective quantum state rather than on individual particles. It is precisely this property that the new measures capture, making it possible to compare completely different experiments on a single scale.
The work shows that modern mechanical systems are already approaching a regime in which quantum effects manifest at the macroscopic level. This opens the way to testing fundamental questions, including possible limits imposed by quantum gravity, and to creating more robust quantum sensors and computing elements.
The results, published in Quantum on 30 October 2026, provide a clear tool for assessing progress in macroscopic quantum mechanics and set new benchmarks for future experiments.
