dorsal/arxiv
View SchemaEntanglement and Symmetry: A Case Study in Superselection Rules, Reference Frames, and Beyond
| Authors | S. J. Jones, H. M. Wiseman, S. D. Bartlett, J. A. Vaccaro, D. T. Pope |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0608056 |
| URL | https://arxiv.org/abs/quant-ph/0608056 |
| DOI | 10.1103/PhysRevA.74.062313 |
| Journal | Phys. Rev. A 74, 062313 (2006) |
Abstract
This paper concentrates on a particular example of a constraint imposed by superselection rules (SSRs): that which applies when the parties (Alice and Bob) cannot distinguish among certain quantum objects they have. This arises naturally in the context of ensemble quantum information processing such as in liquid NMR. We discuss how a SSR for the symmetric group can be applied, and show how the extractable entanglement can be calculated analytically in certain cases, with a maximum bipartite entanglement in an ensemble of N Bell-state pairs scaling as log(N) as N goes to infinity . We discuss the apparent disparity with the asymptotic (N >> 1) recovery of unconstrained entanglement for other sorts of superselection rules, and show that the disparity disappears when the correct notion of applying the symmetric group SSR to multiple copies is used. Next we discuss reference frames in the context of this SSR, showing the relation to the work of von Korff and Kempe [Phys. Rev. Lett. 93, 260502 (2004)]. The action of a reference frame can be regarded as the analog of activation in mixed-state entanglement. We also discuss the analog of distillation: there exist states such that one copy can act as an imperfect reference frame for another copy. Finally we present an example of a stronger operational constraint, that operations must be non-collective as well as symmetric. Even under this stronger constraint we nevertheless show that Bell-nonlocality (and hence entanglement) can be demonstrated for an ensemble of N Bell-state pairs no matter how large N is. This last work is a generalization of that of Mermin [Phys. Rev. D 22, 356 (1980)].
{
"annotation_id": "841acd3e-1a6d-4e84-bed8-bd9fe700f360",
"date_created": "2026-03-02T18:02:30.342000Z",
"date_modified": "2026-03-02T18:02:30.342000Z",
"file_hash": "b5a0c02b9d345b0444a1be353fafb0e94f1ffcd3aa255eae30e9c6bc8b1bb9fc",
"private": false,
"record": {
"abstract": "This paper concentrates on a particular example of a constraint imposed by\nsuperselection rules (SSRs): that which applies when the parties (Alice and\nBob) cannot distinguish among certain quantum objects they have. This arises\nnaturally in the context of ensemble quantum information processing such as in\nliquid NMR. We discuss how a SSR for the symmetric group can be applied, and\nshow how the extractable entanglement can be calculated analytically in certain\ncases, with a maximum bipartite entanglement in an ensemble of N Bell-state\npairs scaling as log(N) as N goes to infinity . We discuss the apparent\ndisparity with the asymptotic (N \u003e\u003e 1) recovery of unconstrained entanglement\nfor other sorts of superselection rules, and show that the disparity disappears\nwhen the correct notion of applying the symmetric group SSR to multiple copies\nis used. Next we discuss reference frames in the context of this SSR, showing\nthe relation to the work of von Korff and Kempe [Phys. Rev. Lett. 93, 260502\n(2004)]. The action of a reference frame can be regarded as the analog of\nactivation in mixed-state entanglement. We also discuss the analog of\ndistillation: there exist states such that one copy can act as an imperfect\nreference frame for another copy. Finally we present an example of a stronger\noperational constraint, that operations must be non-collective as well as\nsymmetric. Even under this stronger constraint we nevertheless show that\nBell-nonlocality (and hence entanglement) can be demonstrated for an ensemble\nof N Bell-state pairs no matter how large N is. This last work is a\ngeneralization of that of Mermin [Phys. Rev. D 22, 356 (1980)].",
"arxiv_id": "quant-ph/0608056",
"authors": [
"S. J. Jones",
"H. M. Wiseman",
"S. D. Bartlett",
"J. A. Vaccaro",
"D. T. Pope"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.74.062313",
"journal_ref": "Phys. Rev. A 74, 062313 (2006)",
"title": "Entanglement and Symmetry: A Case Study in Superselection Rules, Reference Frames, and Beyond",
"url": "https://arxiv.org/abs/quant-ph/0608056"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "b2f95f7c-c55f-44ce-a944-1d96e8dda643",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}