We address the geometric problem of the reconstruction of quantum covariance matrices using the notion of Lagrangian polar duality introduced in previous work. We apply our constructions to Gaussian quantum states which leads to a non-trivial generalization of Pauli's reconstruction problem and we state a tomographic characterization of such states.
https://univienna.zoom.us/j/64895816787?pwd=L0tHVnBPUkJFQVVSR3Y2QnhVRXRGZz09