Quantum States and Hardy’s Formulation of the Uncertainty Principle: a Symplectic Approach
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- de Gosson, M. & Luef, F. Lett Math Phys (2007) 80: 69. doi: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.
Mathematics Subject Classification (2000)81S10 81S30 37J05
KeywordsHardy’s uncertainty principle Wigner distribution density operator positivity
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