dorsal/arxiv
View SchemaUnitarily localizable entanglement of Gaussian states
| Authors | Alessio Serafini, Gerardo Adesso, Fabrizio Illuminati |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0411109 |
| URL | https://arxiv.org/abs/quant-ph/0411109 |
| DOI | 10.1103/PhysRevA.71.032349 |
| Journal | Phys. Rev. A 71, 032349 (2005) |
Abstract
We consider generic $m\times n$-mode bipartitions of continuous variable systems, and study the associated bisymmetric multimode Gaussian states. They are defined as $(m+n)$-mode Gaussian states invariant under local mode permutations on the $m$-mode and $n$-mode subsystems. We prove that such states are equivalent, under local unitary transformations, to the tensor product of a two-mode state and of $m+n-2$ uncorrelated single-mode states. The entanglement between the $m$-mode and the $n$-mode blocks can then be completely concentrated on a single pair of modes by means of local unitary operations alone. This result allows to prove that the PPT (positivity of the partial transpose) condition is necessary and sufficient for the separability of $(m + n)$-mode bisymmetric Gaussian states. We determine exactly their negativity and identify a subset of bisymmetric states whose multimode entanglement of formation can be computed analytically. We consider explicit examples of pure and mixed bisymmetric states and study their entanglement scaling with the number of modes.
{
"annotation_id": "4c1fe270-86cd-4e9d-a485-992b281ad4b7",
"date_created": "2026-03-02T18:02:13.280000Z",
"date_modified": "2026-03-02T18:02:13.280000Z",
"file_hash": "49d020667be1ec40592158522ed0d02b855e9dd9c4176fc0010f60403dba2264",
"private": false,
"record": {
"abstract": "We consider generic $m\\times n$-mode bipartitions of continuous variable\nsystems, and study the associated bisymmetric multimode Gaussian states. They\nare defined as $(m+n)$-mode Gaussian states invariant under local mode\npermutations on the $m$-mode and $n$-mode subsystems. We prove that such states\nare equivalent, under local unitary transformations, to the tensor product of a\ntwo-mode state and of $m+n-2$ uncorrelated single-mode states. The entanglement\nbetween the $m$-mode and the $n$-mode blocks can then be completely\nconcentrated on a single pair of modes by means of local unitary operations\nalone. This result allows to prove that the PPT (positivity of the partial\ntranspose) condition is necessary and sufficient for the separability of $(m +\nn)$-mode bisymmetric Gaussian states. We determine exactly their negativity and\nidentify a subset of bisymmetric states whose multimode entanglement of\nformation can be computed analytically. We consider explicit examples of pure\nand mixed bisymmetric states and study their entanglement scaling with the\nnumber of modes.",
"arxiv_id": "quant-ph/0411109",
"authors": [
"Alessio Serafini",
"Gerardo Adesso",
"Fabrizio Illuminati"
],
"categories": [
"quant-ph",
"cond-mat.other"
],
"doi": "10.1103/PhysRevA.71.032349",
"journal_ref": "Phys. Rev. A 71, 032349 (2005)",
"title": "Unitarily localizable entanglement of Gaussian states",
"url": "https://arxiv.org/abs/quant-ph/0411109"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "3e8efae1-00b8-440f-a499-d717f22fc20e",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}