Symplectic Polar Duality, Quantum Blobs, and Generalized Gaussians
- URL: http://arxiv.org/abs/2206.06334v2
- Date: Tue, 23 Aug 2022 15:32:46 GMT
- Title: Symplectic Polar Duality, Quantum Blobs, and Generalized Gaussians
- Authors: Maurice de Gosson, Charlyne de Gosson
- Abstract summary: We show that quantum blobs are the smallest symplectic invariant regions of the phase space compatible with the uncertainty principle in its strong Robertson--Schr"odinger form.
We show that these phase space units can be characterized by a simple condition of reflexivity using polar duality, thus improving previous results.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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 the phase space
compatible with the uncertainty principle in its strong
Robertson--Schr\"odinger 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.
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