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.
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The authors were supported under the EU-project MEXT-CT-2004-51715.
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de Gosson, M., Luef, F. Quantum States and Hardy’s Formulation of the Uncertainty Principle: a Symplectic Approach. Lett Math Phys 80, 69–82 (2007). https://doi.org/10.1007/s11005-007-0150-6
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DOI: https://doi.org/10.1007/s11005-007-0150-6