Quantum States and Hardy's Formulation of the Uncertainty Principle : a Symplectic Approach

Details Quantum States and Hardy's Formulation of the Uncertainty Principle : a Symplectic Approach Quantum States and Hardy's Formulation of the Uncertainty Principle : a Symplectic Approach

2007-03-07

arxiv.org/abs/quant-ph/0703063v1

Physics

Quantum Physics

To appear in Lett. Math. Phys

Scientific paper

10.1007/s11005-007-0150-6

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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