Compact physical Gaussian-ket models for homodyne quantum-state tomography

Continuous-variable quantum-state tomography usually reconstructs a truncated Fock-basis density matrix. We study a compact alternative: finite mixtures of displaced, squeezed Gaussian kets whose ρ = BB† construction is positive semidefinite by construction, fitted by per-sample homodyne likelihood with closed-form gradients, and composed with physical loss and noise channels. On the public propagating-light GKP dataset of Konno et al. (Science 2024), a rank-4 model with 92 real parameters matches the empirical full-rank maximum-likelihood frontier (255 parameters) at confidence-interval resolution on held-out likelihood. On a synthetic thermal-noise target that we prove lies outside the model family — no detection efficiency and no finite rank reproduces it exactly — the channel-composed model fitted blind exceeds a full-rank MLE run under the pre-declared 900-second baseline budget, a verdict that holds across all five pre-declared seed and noise configurations. We do not claim a universally superior method: comparisons on real data reuse observations across splits, the strongest baseline is test-selected, and the blind result covers one target class. The contribution is a compact, physically constrained model family together with a fully falsification-first research record — negative results, superseded scorings, and pre-declared protocols are all preserved in the accompanying repository.