Entanglement diagnosis stops guessing one label: finite-shot Pauli records yield calibrated verdicts up to 20 qubits

Entanglement-structure judgment becomes a calibrated decision problem: the input is a fixed set of Pauli observables measured with finite shots, and the output is a calibrated statement about multipartite entanglement structure. Full quantum state tomography supplies complete information but scales unfavorably with system size, while entanglement witnesses are often optimized for specific target states or prior assumptions, and many learning-based methods are accuracy-oriented and return a single label even for ambiguous input. On in-distribution benchmarks at N=4, 5 and 6, the global-plus-random and hybrid global-depth strategies gave genuine multipartite entanglement (GME) balanced accuracy close to or equal to 1.000, with empirical coverage near the 0.9 target within finite-sample fluctuations.

The decision layer turns model scores into three outcomes: a single structural label when evidence is strong, a set of plausible labels when it is ambiguous, and abstention when the sample falls outside the calibrated regime. Conformal prediction is a statistical tool that sets thresholds from calibration samples so that prediction sets reach a target coverage; here it is applied per class, and the abstention threshold is set from in-distribution and out-of-distribution calibration samples together. At α=0.1 with target coverage 0.9, adding OOD-calibrated abstention cut overconfident error from 0.790 to 0 for W states and from 0.676 to 0.048 for random-circuit states, at the cost of a final in-distribution accept rate of 0.587.

Measurement design is matched to the task: phase-aware global X/Y-type Pauli probes target GHZ-type coherence, while local and few-body probes serve finer block-structure labels. Random Pauli measurements and global-only designs struggle to capture GHZ phase information under the same small measurement budgets; in the ablation, random strategies were close to random guessing at N=12 and N=20. On the hard perturbed-GHZ benchmark with K=40 observables and 512 shots each, balanced accuracy was 0.968 and overconfident error 0.016 at N=20; in the ablation the phase-aware strategy reached 0.975 and 0.965 at N=12 and N=20, versus 0.686 and 0.672 for global-plus-random.

The demonstrated scope is a synthetic benchmark family: in-distribution experiments cover N=4, 5 and 6, the large-N hard benchmark covers N=8, 10, 12, 16 and 20, and hierarchical structure diagnosis covers N=4 to 8, with measurement budgets of K=40, 80 or 160 and 512 shots per observable. The intended readers are researchers and engineers in quantum-information experiments who must judge entanglement structure from finite Pauli records. The authors propose next steps including tests on noisy many-body ensembles, variational-circuit states, matrix-product states, stabilizer and graph-state families and hardware-generated states, plus adaptive Pauli selection, grouping of compatible observables, device-specific readout calibration and integration with witness-based certification.

Conformal coverage depends on the calibration distribution and the corresponding exchangeability assumption, and the abstention rule's scope is limited to the OOD families represented in calibration. The benchmark state families are mainly synthetic pure states, and the white-noise mixed-state check covers only a first robustness test at η≤0.20. In leave-one-family-out validation, random-circuit states and several N=6 cases transfer less well; for example, held-out random-circuit states at N=6 gave overconfident error 0.503. The K=40 and K=80 observable sets are generated independently rather than nested, so monotonic improvement with K is not guaranteed.