Polar Duality and the Reconstruction of Quantum Covariance Matrices from Partial Data

Abstract

We address the problem of the reconstruction of quantum covariance matrices using the notion of Lagrangian and symplectic 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 simple tomographic characterization of such states.

arXiv commentMinor revisions. To appear in J. Phys. A : Math. Gen