Macroscopic quantum coherence and entanglement in mechanical systems
Abstract
The notion of a macroscopic quantum state must be pinned down in order to assess how well experiments probe the large-scale limits of quantum mechanics. However, the issue of quantifying so-called quantum macroscopicity is fraught with multiple approaches having varying interpretations and levels of computability and measurability. Here, we introduce two measures that capture independent macroscopic properties: i) extensive size, measuring the degree of coherence in position or momentum observables relative to atomic-scale units, and ii) entangled size, quantifying the number of entangled subsystems. These measures unify many desirable features of past proposals while having rigorously justified interpretations from quantum information theory in terms of coherence and multipartite entanglement. We demonstrate how to estimate them and obtain lower-bounds using experimental data from micro-mechanical oscillators and diffracting molecules. Notably, we find evidence for genuine multipartite entanglement of 105 to 107 atoms in recent mechanical superposition states.
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BibTeX
@article{yadin2026macroscopic,
title = {{Macroscopic quantum coherence and entanglement in mechanical systems}},
author = {Benjamin Yadin and Matteo Fadel},
journal = {Quantum},
year = {2026},
month = oct,
doi = {10.22331/q-2026-10-30-2257},
url = {https://quantum-journal.org/papers/q-2026-10-30-2257/},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Macroscopic quantum coherence and entanglement in mechanical systems
AU - Benjamin Yadin
AU - Matteo Fadel
PY - 2026
DA - 2026/10/30
JO - Quantum
DO - 10.22331/q-2026-10-30-2257
UR - https://quantum-journal.org/papers/q-2026-10-30-2257/
AB - The notion of a macroscopic quantum state must be pinned down in order to assess how well experiments probe the large-scale limits of quantum mechanics. However, the issue of quantifying so-called quantum macroscopicity is fraught with multiple approaches having varying interpretations and levels of computability and measurability. Here, we introduce two measures that capture independent macroscopic properties: i) extensive size, measuring the degree of coherence in position or momentum observables relative to atomic-scale units, and ii) entangled size, quantifying the number of entangled subsystems. These measures unify many desirable features of past proposals while having rigorously justified interpretations from quantum information theory in terms of coherence and multipartite entanglement. We demonstrate how to estimate them and obtain lower-bounds using experimental data from micro-mechanical oscillators and diffracting molecules. Notably, we find evidence for genuine multipartite entanglement of 10^5 to 10^7 atoms in recent mechanical superposition states.
SN - 2521-327X
ER -