56 citations · 520 across the 52 of their papers we have counts for
28 papers · 1 filter
On Quantum Indeterminacy and the Uncertainty Principle
Maurice de Gosson
We propose a geometric formulation of quantum indeterminacy based on polar duality between convex bodies representing position and momentum data. A pair (X,P) of centrally symmetri…
Polar Duality and Quasi-States: a Geometric Picture of Quantum Indeterminacy
Maurice de Gosson
The aim of this paper is to suggest a new interpretation of quantum indeterminacy using the notion of polar duality from convex geometry. Our approach does not involve the usual va…
Polar Duality and the Reconstruction of Quantum Covariance Matrices from Partial Data
Maurice A. de Gosson
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 co…
Reconstruction of Gaussian Quantum States from Ideal Position Measurements: Beyond Pauli's Problem, I
Maurice de Gosson
We show that the covariance matrix of a quantum state can be reconstructed from position measurements using the simple notion of polar duality, familiar from convex geometry. In pa…
Pointillisme à la Signac and Construction of a Quantum Fiber Bundle Over Convex Bodies
Maurice de Gosson, Charlyne de Gosson
We use the notion of polar duality from convex geometry and the theory of Lagrangian planes from symplectic geometry to construct a fiber bundle over ellipsoids that can be viewed…
Symplectic Polar Duality, Quantum Blobs, and Generalized Gaussians
Maurice de Gosson, Charlyne de Gosson
We apply the notion of polar duality from convex geometry to the study of quantum covariance ellipsoids in symplectic phase space. We consider in particular the case of "quantum bl…