Researchers have found evidence of genuine multipartite entanglement involving between 10⁵ and 10⁷ atoms within recent mechanical superposition states. Benjamin Yadin of Universität Siegen and Matteo Fadel of Peking University and ETH Zürich developed new measures, “extensive size” and “entangled size”, to quantify macroscopic quantum coherence, moving beyond previously less rigorous approaches.

These measures, grounded in quantum information theory, allow for a transparent comparison of experiments ranging from micro-mechanical oscillators to diffracting molecules, and directly estimate coherence and entanglement from experimental data. The work demonstrates a method for assessing how well experiments probe the large-scale limits of quantum mechanics.

Defining Macroscopic Quantum States & Their Measurement

Recent work introduces a new framework for quantifying macroscopic quantum coherence, moving beyond previously used, less rigorously defined approaches. Extensive size defines the spatial or momentum range over which quantum coherence extends, measured relative to atomic units, while entangled size indicates the number of atoms required to be entangled to account for observed behaviour. These measures allow for direct comparison of experiments and theoretical proposals attempting to create macroscopic quantum states, such as Schrödinger’s cat scenarios.

The researchers applied these measures to data obtained from both micro-mechanical oscillators and diffracting molecules, demonstrating the broad applicability of their quantification methods. The methodology employed isn’t limited to traditional quantum systems; its success with diffracting molecules expands the range of physical phenomena where these quantum effects can be observed and analysed.

As stated in the paper, the goal is to provide a transparent comparison of how close each experiment comes to a true Schrödinger cat, offering a standardized way to evaluate progress in the field. The work builds on earlier attempts to define macroscopic quantum states, referencing E. Schrödinger’s 1935 paper, “Die gegenwärtige Situation in der Quantenmechanik,” and subsequent research exploring the fragility and implementation of such states.

The development of these measures addresses a long-standing challenge in quantum mechanics: the difficulty of objectively assessing the “size” of a macroscopic quantum superposition. The study’s ability to estimate these measures using data from diverse systems represents a step toward a unified understanding of macroscopic quantum behaviour and a more robust framework for future research.

Extensive Size: Quantifying Coherence in Mechanical Systems

The ability to assess macroscopic quantum coherence now relies on newly defined metrics, capturing independent properties of both coherence scale and entanglement level. These measures, termed “extensive size” and “entangled size,” quantify coherence relative to atomic units and the number of entangled subsystems, respectively, offering a unified approach to evaluating quantum macroscopicity. This development moves beyond previous methods by providing rigorously justified interpretations rooted in quantum information theory.

The extensive size specifically measures the distance over which quantum coherence extends in position or momentum, expressed as a multiple of atomic-scale units. By positioning experiments and theoretical proposals on these two axes, researchers can achieve a transparent comparison of how closely each approaches a genuine Schrödinger cat state, a superposition of macroscopically distinct states.

The researchers note that system size inherently limits coherence, as the number of environmental coupling channels increases with scale, demanding ever-greater precision for detection. However, the work suggests these are primarily technical hurdles, leaving open the possibility that fundamental physics, such as effects from quantum gravity, may ultimately set a limit on the size of achievable quantum superpositions. The current approach, however, aims for a more comprehensive and quantifiable assessment of macroscopic quantum behavior.

As stated in the paper, “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.” The team’s methodology also draws on earlier work by Braunstein and Caves, published in 1994, but moves beyond statistical distance-based approaches. The researchers’ work, published in Quantum, builds on the foundation laid by E.

Entangled Size: Assessing Multipartite Entanglement Levels

The quantification of macroscopic quantum coherence now extends to assessing the degree of entanglement within a system, with new measures revealing evidence of up to 10⁷ atoms linked in mechanical superposition states. Researchers developed two new metrics, “extensive size” and “entangled size”, to capture independent macroscopic properties, allowing for a comparative assessment of quantum coherence across different experimental setups. The ability to apply these measures across diverse physical platforms is significant because it establishes a unified analytical framework for quantum coherence.

This observation challenges the conventional understanding that quantum effects diminish rapidly with increasing system size, suggesting that mechanical systems may be capable of sustaining entanglement across a far greater number of particles than previously thought. The study’s methodology allows for the estimation of these measures using experimental data, providing a pathway toward a universal language for describing macroscopic quantum coherence. Schrödinger, “Die gegenwärtige Situation in der Quantenmechanik,” while offering a new, quantifiable approach to understanding the limits of quantum mechanics.

Experimental Evidence of 10⁵ to 10⁷ Atom Entanglement

The researchers successfully estimated key metrics using data gathered from both micro-mechanical oscillators and, unexpectedly, diffracting molecules, broadening the scope of quantum coherence studies. These metrics allow for a direct comparison of experiments, ranging from trapped ions to the more complex mechanical systems, by assessing the spatial or momentum scale over which quantum coherence persists. The “entangled size” specifically quantifies the number of atoms contributing to the observed entanglement, providing a more granular understanding of the system’s quantum properties.

Challenges to Maintaining Quantum Coherence with Scale

This discovery, detailed in Quantum, demonstrates entanglement in systems far exceeding those typically associated with quantum phenomena, challenging conventional understandings of coherence limits. Entangled size, conversely, quantifies the number of entangled subsystems necessary to explain observed behaviour, offering a novel way to assess the degree of multipartite entanglement. The work acknowledges that maintaining quantum coherence in larger systems is not merely a technical hurdle, but may also be subject to fundamental limits imposed by as-yet-unknown physics, such as effects stemming from quantum gravity.

The precision required to detect quantum behaviour becomes increasingly demanding as system size increases, as the number of potential coupling channels to the environment grows. However, the current work suggests these challenges may not be insurmountable, and that a deeper understanding of the interplay between system size, coherence, and entanglement is within reach.

👉 More information
🗞 Macroscopic quantum coherence and entanglement in mechanical systems
✍️ Benjamin Yadin and Matteo Fadel
🧠 DOI: https://quantum-journal.org/papers/q-2026-10-30-2257/

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