Equality of morphology and shell-witness noise thresholds

Determine whether visible morphology and Gaussian shell witnesses associated with the selected wave number fail at the same physical noise level in the completely positive Lindblad model of quantum Turing patterns.

Background

The paper studies a completely positive Lindblad model of parametrically driven nonlinear bosonic resonators that supports quantum Turing patterns, including stable stripe morphologies. It compares first-moment morphology, particularly visible stripe order, with Gaussian covariance witnesses evaluated on the same selected wave-number shell k*.

The unresolved issue concerns whether these two sectors lose their respective signatures at a common physical noise threshold. The paper investigates this question and reports parametrically separated thresholds: Gaussian witness crossings occur at noise levels of order the inverse local-noise parameter, whereas the stripe morphology threshold approaches a nonzero limit under the stated fixed-size, fixed-time-window, and fixed-morphology-criterion conditions.