Quantum States and Hardy's Formulation of the Uncertainty Principle : a Symplectic Approach
Quantum Physics
2009-11-13 v1
Abstract
We express the condition for a phase space Gaussian to be the Wigner distribution of a mixed quantum state in terms of the symplectic capacity of the associated Wigner ellipsoid. Our results are motivated by Hardy's formulation of the uncertainty principle for a function and its Fourier transform. As a consequence we are able to state a more general form of Hardy's theorem.
Keywords
Cite
@article{arxiv.quant-ph/0703063,
title = {Quantum States and Hardy's Formulation of the Uncertainty Principle : a Symplectic Approach},
author = {Maurice de Gosson and Franz Luef},
journal= {arXiv preprint arXiv:quant-ph/0703063},
year = {2009}
}
Comments
To appear in Lett. Math. Phys