dorsal/arxiv
View SchemaEntangled subspaces and quantum symmetries
| Authors | A. J. Bracken |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0304132 |
| URL | https://arxiv.org/abs/quant-ph/0304132 |
| DOI | 10.1103/PhysRevA.69.052331 |
Abstract
Entanglement is defined for each vector subspace of the tensor product of two finite-dimensional Hilbert spaces, by applying the notion of operator entanglement to the projection operator onto that subspace. The operator Schmidt decomposition of the projection operator defines a string of Schmidt coefficients for each subspace, and this string is assumed to characterize the entanglement of the subspace, so that a first subspace is more entangled than a second, if the Schmidt string of the second subspace majorizes the Schmidt string of the first. The idea is applied to the antisymmetric and symmetric tensor products of a finite-dimensional Hilbert space with itself, and also to the tensor product of an angular momentum j with a spin 1/2. When adapted to the subspaces of states of the nonrelativistic hydrogen atom with definite total angular momentum (orbital plus spin), within the space of bound states with a given total energy, this leads to a complete ordering of those subspaces by their Schmidt strings.
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"abstract": "Entanglement is defined for each vector subspace of the tensor product of two\nfinite-dimensional Hilbert spaces, by applying the notion of operator\nentanglement to the projection operator onto that subspace. The operator\nSchmidt decomposition of the projection operator defines a string of Schmidt\ncoefficients for each subspace, and this string is assumed to characterize the\nentanglement of the subspace, so that a first subspace is more entangled than a\nsecond, if the Schmidt string of the second subspace majorizes the Schmidt\nstring of the first. The idea is applied to the antisymmetric and symmetric\ntensor products of a finite-dimensional Hilbert space with itself, and also to\nthe tensor product of an angular momentum j with a spin 1/2. When adapted to\nthe subspaces of states of the nonrelativistic hydrogen atom with definite\ntotal angular momentum (orbital plus spin), within the space of bound states\nwith a given total energy, this leads to a complete ordering of those subspaces\nby their Schmidt strings.",
"arxiv_id": "quant-ph/0304132",
"authors": [
"A. J. Bracken"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.69.052331",
"title": "Entangled subspaces and quantum symmetries",
"url": "https://arxiv.org/abs/quant-ph/0304132"
},
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