Tomography of approximately Gaussian mixed states

arXiv:2611.09322v1 Announce Type: new Abstract: Moment-based tomography efficiently reconstructs Gaussian states, but stochastic phase noise generally produces mixed, non-Gaussian outputs. For approximately Gaussian outputs, we formulate reconstruction as a problem in quantum learning theory under model misspecification. Our trace-distance guarantee separates the intrinsic Gaussian approximation error from statistical errors in estimating the first moments and covariance matrix. Using recent Gaussian trace-distance bounds, we obtain linear dependence of the statistical contribution on moment errors when the covariance inverses remain bounded, improving on the square-root dependence on covariance error in earlier guarantees.