The Pauli Problem for Gaussian Quantum States: Geometric Interpretation

Maurice A. de Gosson
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Maurice A. de Gosson: Faculty of Mathematics (NuHAG), University of Vienna, 1090 Vienna, Austria

Mathematics, 2021, vol. 9, issue 20, 1-9

Abstract: We solve the Pauli tomography problem for Gaussian signals using the notion of Schur complement. We relate our results and method to a notion from convex geometry, polar duality. In our context polar duality can be seen as a sort of geometric Fourier transform and allows a geometric interpretation of the uncertainty principle and allows to apprehend the Pauli problem in a rather simple way.

Keywords: covriance matrix; polar duality; uncertainty principle; reconstruction problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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