dorsal/arxiv
View SchemaFinite-level systems, Hermitian operators, isometries, and a novel parameterization of Stiefel and Grassmann manifolds
| Authors | Petre Dita |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0305156 |
| URL | https://arxiv.org/abs/quant-ph/0305156 |
| DOI | 10.1088/0305-4470/38/12/008 |
| Journal | J.Phys. A38 (2005) 2657-2668 |
Abstract
In this paper we obtain a description of the Hermitian operators acting on the Hilbert space $\C^n$, description which gives a complete solution to the over parameterization problem. More precisely we provide an explicit parameterization of arbitrary $n$-dimensional operators, operators that may be considered either as Hamiltonians, or density matrices for finite-level quantum systems. It is shown that the spectral multiplicities are encoded in a flag unitary matrix obtained as an ordered product of special unitary matrices, each one generated by a complex $n-k$-dimensional unit vector, $k=0,1,...,n-2$. As a byproduct, an alternative and simple parameterization of Stiefel and Grassmann manifolds is obtained.
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"abstract": "In this paper we obtain a description of the Hermitian operators acting on\nthe Hilbert space $\\C^n$, description which gives a complete solution to the\nover parameterization problem. More precisely we provide an explicit\nparameterization of arbitrary $n$-dimensional operators, operators that may be\nconsidered either as Hamiltonians, or density matrices for finite-level quantum\nsystems. It is shown that the spectral multiplicities are encoded in a flag\nunitary matrix obtained as an ordered product of special unitary matrices, each\none generated by a complex $n-k$-dimensional unit vector, $k=0,1,...,n-2$. As a\nbyproduct, an alternative and simple parameterization of Stiefel and Grassmann\nmanifolds is obtained.",
"arxiv_id": "quant-ph/0305156",
"authors": [
"Petre Dita"
],
"categories": [
"quant-ph",
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],
"doi": "10.1088/0305-4470/38/12/008",
"journal_ref": "J.Phys. A38 (2005) 2657-2668",
"title": "Finite-level systems, Hermitian operators, isometries, and a novel parameterization of Stiefel and Grassmann manifolds",
"url": "https://arxiv.org/abs/quant-ph/0305156"
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