Fixed-order postselected CHSH reference acquisition for parity-constrained spatial-mode qubits on a commercial cloud photonic processor
We report a fixed-order Clauser-Horne-Shimony-Holt (CHSH) acquisition and reporting protocol for two encoded photonic qubits on Quandela's commercial, cloud-accessible Belenos processor, executed end-to-end by external users through the public cloud interface. Each logical qubit is a two-dimensional spatial-mode subspace in the seven-dimensional zero-sum sector of an eight-mode single-photon register, and a target postselected linear-optical controlled-$Z$ (ideal success probability $1/9$) couples the registers on $16$ of $24$ modes. The primary quantity is the operational CHSH score $S$ on accepted logical coincidences, with each complete four-setting pass as the experimental unit. Eight sequential same-day passes each gave a raw score above $2$; session means were $2.40$ and $2.58$ (sample standard deviations $0.15$ and $0.03$), with excess dispersion $Q/\nu=6.1$ ($\nu=7$). Count-pooled secondary descriptors are $S_{\mathrm{count}}=2.485\pm0.019$ and a fixed-ratio efficiency-reweighted model scenario $S^{\mathrm{rw}}_{\mathrm{count}}=2.380\pm0.021$, whose weakest reweighted pass ($2.040\pm0.062$) overlapped $2$ within $1\sigma$. The reweighting is an archived-metadata model scenario, not a corrected platform score; an ad hoc $\kappa\in[1.2,1.8]$ stress scan (not a calibrated uncertainty band) spans $2.341$-$2.441$. Setting order was fixed, the compiled mapping was not returned, and residual remote-setting marginals remain, so the data support an operational reference acquisition rather than an entanglement-witness or cross-platform benchmarking claim. The parity-check terminology labels the encoding subspace; no syndrome measurement was performed. Count records, job identifiers, circuit-construction code, and analysis are openly archived with content hashes for the submitted targets.