A computational study reports that stripe-like order in a simulated quantum lattice persisted after two tested Gaussian witnesses—mathematical checks built from covariance, the model’s record of linked fluctuations—had crossed zero. At the reported scale, the morphology threshold was about 54 times the NPT threshold, and resolved stripes remained after both exact-shell witness margins crossed zero.
The study asks whether the point at which a pattern loses its shape is the same as the point at which shell witnesses lose their signal. It uses a completely positive Lindblad generator—the model’s rule for evolution with gain, loss and noise—with one-photon gain and loss, two-photon loss, and a single model fixing both drift and diffusion.
One equation, several patterns
The same Lindblad equation supported an atlas of stripes, spots, holes, labyrinths and defects. For the stripe crossover, the study used an ensemble mean nematicity of 0.72—a measure of directional order—while tracking real-space contrast and Bragg concentration separately.
The tests did not fail together
The two leading exact-k* shell tests, focused on a selected momentum shell, crossed at nearly the same bath occupation, the model’s setting for thermal noise: about 1.02 for NPT and 1.04 for the second-moment P witness. The crossings were reported as unchanged to numerical precision across the tested commensurate lattices.
But the physical-noise thresholds split apart. The paper reports that Gaussian-witness thresholds fell roughly as the inverse of N, while the morphology threshold approached a nonzero limit. The long-time finite-N morphology threshold was about 1.64 × 10−2 noise units, compared with about 1.60 × 10−2 for the fixed-size large-N limit.
The uncertainty check used a percentile bootstrap with 5,000 trajectory-level resamples. It put the finite-N morphology estimate in a 95% interval of [1.58, 1.71] × 10−2 and the large-N estimate in [1.56, 1.67] × 10−2; the ranges overlap, but the estimates remain distinct.
More than a pairwise signal
In a tested Bloch sector, full-sector covariance negativity stayed nonzero after the pairwise exact-shell witnesses had crossed zero. The result is limited to that tested sector; it does not establish the same behavior for every sector.
The principal and horizontal stripe branches also retained nonzero covariance asymmetry after the ky = 0 sector containing the nearly neutral translation mode was removed. At zero bath occupation, the reported asymmetry fractions were 0.34 for the principal stripe and 0.47 for the horizontal stripe.
A calculation with defined boundaries
A feedback control did not erase the separation. Of 38 initially Hurwitz-stable uniform phases, 35 remained in the stability domain; the stripe NPT crossing was about 1.91, versus 2.15 to 2.25 for surviving uniform comparison states. Exact-shell crossings shifted by less than 0.3%.
The boundaries of the calculation matter. The morphology threshold uses the 0.72 nematicity cutoff, while the Gaussian result concerns the tested exact-k* pair witnesses and selected covariance sectors. The findings therefore describe this Lindblad model and these diagnostics, not every possible nonclassicality measure.
The evidence is computational, based on a finite-N trajectory ensemble alongside a fixed-size large-N limiting calculation. The authors state that code is available in a GitHub repository and that reproduction data may be available upon reasonable request.
The document is identified as arXiv:2608.20151v1, dated 20 Aug 2026, and presented as a preprint.
Paper data and sources
Original title: A Zoology of Quantum Turing Patterns
Authors: Kazuki Ikeda
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
Original paper · Full text