Certifying Macroscopic Quantum Coherence

Research on macroscopic superpositions asks which experimentally accessible degrees of freedom maintain coherence between distinguishable alternatives, for how long, and against which alternative models. Mass, spatial separation, constituent number, and phase-space distance are different quantities. Reviewed 11 October 2026, this assessment includes the January 2026 nanoparticle-interferometry report alongside the cited conceptual literature. It compares what experiments certify rather than asserting a universal latest-platform ranking.

Helpful background. Macroscopic superpositions gives the stable coherence criteria. Massive superpositions addresses center-of-mass mass, isolation, and gravity-related platform constraints.

Coherence certification before scale comparison

For orthogonal branches, an effective state is

$$\rho= \begin{pmatrix} p&c\\ c^*&1-p \end{pmatrix}, \qquad |c|^2\le p(1-p).$$

A mixture has $c=0$ even if both branch populations are large. A phase-sensitive measurement or calibrated witness must constrain $c$; a photograph of two spatial populations does not.

For ideal balanced recombination, $P_+(\phi)=1/2+\operatorname{Re}(ce^{i\phi})$. Thus visibility is $2|c|$ in this restricted model. Real losses, fluctuating phases, imperfect overlap, and detector response alter the inference. An operational macroscopicity comparison must identify the model of modification being excluded or the task for which the state is useful.

Phase averaging can imitate irreversible decay

Suppose the phase in the recombination formula has an unrecorded random offset $\delta\phi$ drawn independently from a zero-mean Gaussian of variance $\sigma_\phi^2$. Averaging gives $\mathbb E[e^{i\delta\phi}]=e^{-\sigma_\phi^2/2}, \qquad V_{\mathrm{obs}}=2|c|e^{-\sigma_\phi^2/2}.$ This is an ensemble statement. It does not determine whether individual systems lost coherence irreversibly, or whether a phase reference was lost between shots. For example, $\sigma_\phi=1$ radian lowers visibility by a factor of about $0.607$ without changing the within-shot state in this model. Independent phase monitoring can distinguish that mechanism from an additional unmonitored localization process only to the extent that the monitor resolves the relevant fluctuations.

A detector model also matters. With a constant additive background, fitting raw counts to $A+B\cos\phi$ gives visibility $|B|/A$; subtracting an uncertain background changes the inferred visibility and its uncertainty. A defensible coherence claim uses a likelihood for counts, backgrounds, and accepted events, rather than treating the fitted visibility as an exact off-diagonal element.

What is established and what remains open?

Quantum interference and engineered cat states are established in specified systems. Their existence supports coherent dynamics in those systems; it does not supply a universal scale beyond which quantum mechanics either fails or must survive. Collapse models offer explicit departures whose parameters can be constrained, while ordinary environmental decoherence can produce similar reductions in visibility.

Pedalino and colleagues’ 2026 experiment provides a useful concrete comparison. Sodium clusters around 172 kDa showed fringes whose dependence on grating laser power distinguished the quantum prediction from the specified classical trajectory model. The same report found stronger fringes for 400 kDa–1 MDa clusters, but in that apparatus regime quantum and classical predictions were too similar for that stronger contrast to establish a larger quantum-superposition result. The discriminating dependence, not visibility alone, supplies the evidence.

Nimmrichter and Hornberger define an operational macroscopicity measure through the modification class an experiment excludes. Its value depends on a specified dynamical comparison and cannot be interchanged with mass, particle number, or a quantum Fisher information without explanation. Schlosshauer provides the decoherence baseline. Bassi, Dorato, and Ulbricht emphasize that collapse parameters connect differently to each experimental configuration. These perspectives motivate a discriminating question: can a chosen platform vary a control parameter that affects a proposed fundamental process differently from known noise?

Three useful directions are calibration-robust coherence witnesses; transparent comparison of macroscopicity measures; and controlled changes of separation, geometry, temperature, or duration that distinguish decoherence mechanisms. Large headline scale without such discrimination can be less informative than a smaller but cleaner experiment.

A two-setting identifiability calculation

Let a control setting $j$ change the hypothesized localization contribution by a known dimensionless factor $g_j$. Under a common environmental rate and independently calibrated initial contrast, define $r_j=-\frac1{t_j}\log\frac{V_j}{V_{0j}} =\Gamma_{\mathrm{env}}+\kappa g_j.$ Two settings with $g_1\ne g_2$ give $\kappa=\frac{r_2-r_1}{g_2-g_1}, \qquad \Gamma_{\mathrm{env}}= \frac{g_2r_1-g_1r_2}{g_2-g_1}.$ If the fitted rates have independent equal variance $\sigma_r^2$, then $\operatorname{Var}\hat\kappa=2\sigma_r^2/(g_2-g_1)^2$. Nearly identical responses give poor inference even with a formally invertible model.

The crucial physics is whether changing $g_j$ also changes the ordinary environment. If the environmental rate is allowed to vary freely at each setting, two rates cannot identify three unknowns. The research target is an experimentally justified control or calibration that removes that ambiguity. The displayed inversion is only the baseline.

An entry project: identify what a visibility curve actually excludes

Baseline. Generate two-path interference data with known contrast and phase noise. Fit a model with environmental dephasing rate $\Gamma_{\mathrm{env}}$ and an additional localization contribution $\Gamma_{\mathrm{loc}}$:

$$V(t)=V_0\exp[-(\Gamma_{\mathrm{env}}+\Gamma_{\mathrm{loc}})t].$$

At a single setting only the sum is identifiable. Demonstrating this degeneracy is the first checkpoint.

Resources. A laptop, likelihood fitting, density matrices, and a documented noise model are sufficient. An experimental collaboration is needed only for a real instrument-specific inference.

Deliverable. Introduce a second experimentally motivated control dependence and produce confidence regions for both rates, with nuisance parameters profiled or marginalized explicitly. Compare exclusion with and without an independent noise calibration. Reproduce the two-setting inversion above before allowing nonlinear detector response. If using the nanoparticle report, compare quantum and classical predictions over the power scan with the same mass and velocity distributions and nuisance freedom.

Failure criterion. If the fitted extra rate is explained by modest drift in $V_0$ or the environmental model, do not report evidence for a dynamical modification. Check that the synthetic-data confidence procedure has its declared coverage.

Research extension. Design an observable or control schedule maximizing discrimination between two explicit mechanisms at fixed total measurement time. Include preparation failure, dead time, and systematic uncertainty rather than optimizing ideal contrast alone.

Project choice and update triggers

Choose a witness project when readout dominates uncertainty; choose noise identification when preparation is established but interpretation is ambiguous; choose cross-platform comparison when published data expose compatible operational quantities. A new coherence record should change the assessment only with the certified observable and its limitations attached.

Do not infer a single outcome mechanism from suppression of interference. Measurement-problem research addresses that separate conceptual issue, while collapse tests addresses specified dynamical models.

References

• A. Bassi, M. Dorato, and H. Ulbricht, “Collapse Models: A Theoretical, Experimental and Philosophical Review,” Entropy 25, 645 (2023). Open article.
• S. Nimmrichter and K. Hornberger, “Macroscopicity of Mechanical Quantum Superposition States,” Physical Review Letters 110, 160403 (2013). Operational measure.
• S. Pedalino, B. E. Ramírez-Galindo, R. Ferstl, K. Hornberger, M. Arndt, and S. Gerlich, “Probing quantum mechanics with nanoparticle matter-wave interferometry,” Nature 649, 866–870 (2026). Primary report and methods.
• M. Schlosshauer, “Decoherence, the measurement problem, and interpretations of quantum mechanics,” Reviews of Modern Physics 76, 1267–1305 (2004). arXiv:quant-ph/0312059.

Entry points

Reconstruct a published witness from its detector model before reading cross-platform rankings. Ask which off-diagonal matrix element or nonclassical inequality the measurement actually constrains.