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Keywords = John ellipsoid

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17 pages, 322 KB  
Article
Symplectic Polar Duality, Quantum Blobs, and Generalized Gaussians
by Maurice de Gosson and Charlyne de Gosson
Symmetry 2022, 14(9), 1890; https://doi.org/10.3390/sym14091890 - 9 Sep 2022
Cited by 3 | Viewed by 1973
Abstract
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 blobs” introduced in previous work; quantum blobs are the smallest symplectic invariant regions of [...] Read more.
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 blobs” introduced in previous work; quantum blobs are the smallest symplectic invariant regions of the phase space compatible with the uncertainty principle in its strong Robertson–Schrödinger form. We show that these phase space units can be characterized by a simple condition of reflexivity using polar duality, thus improving previous results. We apply these geometric constructions to the characterization of pure Gaussian states in terms of partial information on the covariance ellipsoid, which allows us to formulate statements related to symplectic tomography. Full article
(This article belongs to the Topic Quantum Information and Quantum Computing)
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