dorsal/arxiv
View SchemaTomography in abstract Hilbert spaces
| Authors | V. I. Man'ko, G. Marmo, A. Simoni, F. Ventriglia |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0604039 |
| URL | https://arxiv.org/abs/quant-ph/0604039 |
Abstract
The tomographic description of a quantum state is formulated in an abstract infinite dimensional Hilbert space framework, the space of the Hilbert-Schmidt linear operators, with trace formula as scalar product. Resolutions of the unity, written in terms of over-complete sets of rank-one projectors and of associated Gram-Schmidt operators taking into account their non-orthogonality, are then used to reconstruct a quantum state from its tomograms. Examples of well known tomographic descriptions illustrate the exposed theory.
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"abstract": "The tomographic description of a quantum state is formulated in an abstract\ninfinite dimensional Hilbert space framework, the space of the Hilbert-Schmidt\nlinear operators, with trace formula as scalar product. Resolutions of the\nunity, written in terms of over-complete sets of rank-one projectors and of\nassociated Gram-Schmidt operators taking into account their non-orthogonality,\nare then used to reconstruct a quantum state from its tomograms. Examples of\nwell known tomographic descriptions illustrate the exposed theory.",
"arxiv_id": "quant-ph/0604039",
"authors": [
"V. I. Man\u0027ko",
"G. Marmo",
"A. Simoni",
"F. Ventriglia"
],
"categories": [
"quant-ph",
"hep-th",
"math-ph",
"math.MP"
],
"title": "Tomography in abstract Hilbert spaces",
"url": "https://arxiv.org/abs/quant-ph/0604039"
},
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