dorsal/arxiv
View SchemaQuantum States and Hardy's Formulation of the Uncertainty Principle : a Symplectic Approach
| Authors | Maurice de Gosson, Franz Luef |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0703063 |
| URL | https://arxiv.org/abs/quant-ph/0703063 |
| DOI | 10.1007/s11005-007-0150-6 |
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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"abstract": "We express the condition for a phase space Gaussian to be the Wigner\ndistribution of a mixed quantum state in terms of the symplectic capacity of\nthe associated Wigner ellipsoid. Our results are motivated by Hardy\u0027s\nformulation of the uncertainty principle for a function and its Fourier\ntransform. As a consequence we are able to state a more general form of Hardy\u0027s\ntheorem.",
"arxiv_id": "quant-ph/0703063",
"authors": [
"Maurice de Gosson",
"Franz Luef"
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"doi": "10.1007/s11005-007-0150-6",
"title": "Quantum States and Hardy\u0027s Formulation of the Uncertainty Principle : a Symplectic Approach",
"url": "https://arxiv.org/abs/quant-ph/0703063"
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