dorsal/arxiv
View SchemaDiscrete Q- and P-symbols for spin s
| Authors | Jean-Pierre Amiet, Stefan Weigert |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9906099 |
| URL | https://arxiv.org/abs/quant-ph/9906099 |
| DOI | 10.1088/1464-4266/2/2/309 |
| Journal | J.Opt. B2 (2000) 118 |
Abstract
Non-orthogonal bases of projectors on coherent states are introduced to expand hermitean operators acting on the Hilbert space of a spin s. It is shown that the expectation values of a hermitean operator A in a family of (2s+1)(2s+1) spin-coherent states determine the operator unambiguously. In other words, knowing the Q-symbol of A at (2s+1)(2s+1) points on the unit sphere is already sufficient in order to recover the operator. This provides a straightforward method to reconstruct the mixed state of a spin since its density matrix is explicitly parametrized in terms of expectation values. Furthermore, a discrete P-symbol emerges naturally which is related to a basis dual to the original one.
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"abstract": "Non-orthogonal bases of projectors on coherent states are introduced to\nexpand hermitean operators acting on the Hilbert space of a spin s. It is shown\nthat the expectation values of a hermitean operator A in a family of\n(2s+1)(2s+1) spin-coherent states determine the operator unambiguously. In\nother words, knowing the Q-symbol of A at (2s+1)(2s+1) points on the unit\nsphere is already sufficient in order to recover the operator. This provides a\nstraightforward method to reconstruct the mixed state of a spin since its\ndensity matrix is explicitly parametrized in terms of expectation values.\nFurthermore, a discrete P-symbol emerges naturally which is related to a basis\ndual to the original one.",
"arxiv_id": "quant-ph/9906099",
"authors": [
"Jean-Pierre Amiet",
"Stefan Weigert"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/1464-4266/2/2/309",
"journal_ref": "J.Opt. B2 (2000) 118",
"title": "Discrete Q- and P-symbols for spin s",
"url": "https://arxiv.org/abs/quant-ph/9906099"
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