A Gaussian-Pointer Testbed for Coarse-Grained Quantum Instruments and Controlled Deviations from Lüders Updating

A reproducible simulation testbed for instrument-level quantum measurement modeling. Using a standard von Neumann Gaussian pointer coupled to a diagonal observable, followed by classical Gaussian readout blur and midpoint binning with optional outcome merges, this work constructs explicit coarse-grained quantum instruments and quantifies when a reported “subspace outcome” is or is not well-approximated by Lüders updating. The main study uses a three-level system with two nearly degenerate eigenvalues. We sweep a near-degeneracy parameter ε∈[0,1]\varepsilon\in[0,1]ε∈[0,1] and a dimensionless coupling strength s∈[0.25,12]s\in[0.25,12]s∈[0.25,12], compare the instrument-conditioned post-measurement state to the corresponding Lüders-updated state, and measure the mismatch via trace distance. The key empirical result is that mismatch data collapse strongly onto a single within-subspace distinguishability coordinate derived from the pointer overlap γ12\gamma_{12}γ12 between the nearly degenerate branches. For the released run (mixed-state ensemble, N=800N=800N=800, σ=1\sigma=1σ=1, readout blur σr∈{0,0.5,1}\sigma_r\in\{0,0.5,1\}σr∈{0,0.5,1}), the normalized mismatch is well described by the minimal turn-on model y(γ)=y∞(1−γ b)y(\gamma)=y_\infty(1-\gamma^{\,b})y(γ)=y∞(1−γb) with overall best-fit y∞≈0.248y_\infty\approx 0.248y∞≈0.248, b≈1.06b\approx 1.06b≈1.06 and R2≈0.994R^2\approx 0.994R2≈0.994 (pooled over σr\sigma_rσr). Additional residual diagnostics indicate structured departures consistent with secondary parameters (imbalance and additional overlaps) beyond the one-parameter reduction. This deposit contains: run configuration and summaries, the full set of raw aggregate results (\texttt{raw/**/aggregate.npz}), processed analysis tables and fit summaries, and the figure PDFs used in the manuscript (collapse scatter, binned fit, and residual diagnostics). Together these files allow independent verification of the reported fit parameters and reproduction of the cited figures without requiring access to proprietary data or hardware.