  We propose a method for stably removing noise from measurements of a quantum
many-body system. The question is cast to a linear inverse problem by using a
quantum Fischer information metric as figure of merit. This requires the
ability to compute the adjoint of the noise channel with respect to the metric,
which can be done analytically when the metric is evaluated at a Gaussian
(quasi-free) state. This approach can be applied effectively to n-point
functions of a quantum field theory. For translation invariant noise, this
yields a stable deconvolution method on the first moments of the field which
differs from what one would obtain from a purely classical analysis.
