Gaussian kernel and point-pair coherence

For a pure Gaussian, ${\mathcal{V}}_{\mathrm{pair}}=1$. This does not imply high-probability preparation at every separation, nor resolved fringes after a real detector.

A decomposition $Y=Y_{\mathrm{pre}}+Y_{\mathrm{post}}+Y_{\mathrm{readout}}$ requires multiplicative visibility factorization or a controlled approximation. It is not a general identity for successive quantum instruments.