dorsal/arxiv
View SchemaRadon transform and pattern functions in quantum tomography
| Authors | Alfred Wünsche |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9706024 |
| URL | https://arxiv.org/abs/quant-ph/9706024 |
| DOI | 10.1080/09500349708231885 |
Abstract
The two-dimensional Radon transform of the Wigner quasiprobability is introduced in canonical form and the functions playing a role in its inversion are discussed. The transformation properties of this Radon transform with respect to displacement and squeezing of states are studied and it is shown that the last is equivalent to a symplectic transformation of the variables of the Radon transform with the contragredient matrix to the transformation of the variables in the Wigner quasiprobability. The reconstruction of the density operator from the Radon transform and the direct reconstruction of its Fock-state matrix elements and of its normally ordered moments are discussed. It is found that for finite-order moments the integration over the angle can be reduced to a finite sum over a discrete set of angles. The reconstruction of the Fock-state matrix elements from the normally ordered moments leads to a new representation of the pattern functions by convergent series over even or odd Hermite polynomials which is appropriate for practical calculations. The structure of the pattern functions as first derivatives of the products of normalizable and nonnormalizable eigenfunctions to the number operator is considered from the point of view of this new representation.
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"abstract": "The two-dimensional Radon transform of the Wigner quasiprobability is\nintroduced in canonical form and the functions playing a role in its inversion\nare discussed. The transformation properties of this Radon transform with\nrespect to displacement and squeezing of states are studied and it is shown\nthat the last is equivalent to a symplectic transformation of the variables of\nthe Radon transform with the contragredient matrix to the transformation of the\nvariables in the Wigner quasiprobability. The reconstruction of the density\noperator from the Radon transform and the direct reconstruction of its\nFock-state matrix elements and of its normally ordered moments are discussed.\nIt is found that for finite-order moments the integration over the angle can be\nreduced to a finite sum over a discrete set of angles. The reconstruction of\nthe Fock-state matrix elements from the normally ordered moments leads to a new\nrepresentation of the pattern functions by convergent series over even or odd\nHermite polynomials which is appropriate for practical calculations. The\nstructure of the pattern functions as first derivatives of the products of\nnormalizable and nonnormalizable eigenfunctions to the number operator is\nconsidered from the point of view of this new representation.",
"arxiv_id": "quant-ph/9706024",
"authors": [
"Alfred W\u00fcnsche"
],
"categories": [
"quant-ph"
],
"doi": "10.1080/09500349708231885",
"title": "Radon transform and pattern functions in quantum tomography",
"url": "https://arxiv.org/abs/quant-ph/9706024"
},
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