dorsal/arxiv
View SchemaOn the number of representations providing noiseless subsystems
| Authors | William Gordon Ritter |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0511166 |
| URL | https://arxiv.org/abs/quant-ph/0511166 |
| DOI | 10.1103/PhysRevA.72.062328 |
| Journal | Phys. Rev. A 72, 062328 (2005) |
Abstract
This paper studies the combinatoric structure of the set of all representations, up to equivalence, of a finite-dimensional semisimple Lie algebra. This has intrinsic interest as a previously unsolved problem in representation theory, and also has applications to the understanding of quantum decoherence. We prove that for Hilbert spaces of sufficiently high dimension, decoherence-free subspaces exist for almost all representations of the error algebra. For decoherence-free subsystems, we plot the function $f_d(n)$ which is the fraction of all $d$-dimensional quantum systems which preserve $n$ bits of information through DF subsystems, and note that this function fits an inverse beta distribution. The mathematical tools which arise include techniques from classical number theory.
{
"annotation_id": "986d7ab9-1507-45c9-8e1e-c3e1060148b2",
"date_created": "2026-03-02T18:02:23.884000Z",
"date_modified": "2026-03-02T18:02:23.884000Z",
"file_hash": "66899d1520bff03bb2de1da48e2aa886f243dc89e48de89a099a7e34f95d0de8",
"private": false,
"record": {
"abstract": "This paper studies the combinatoric structure of the set of all\nrepresentations, up to equivalence, of a finite-dimensional semisimple Lie\nalgebra. This has intrinsic interest as a previously unsolved problem in\nrepresentation theory, and also has applications to the understanding of\nquantum decoherence. We prove that for Hilbert spaces of sufficiently high\ndimension, decoherence-free subspaces exist for almost all representations of\nthe error algebra. For decoherence-free subsystems, we plot the function\n$f_d(n)$ which is the fraction of all $d$-dimensional quantum systems which\npreserve $n$ bits of information through DF subsystems, and note that this\nfunction fits an inverse beta distribution. The mathematical tools which arise\ninclude techniques from classical number theory.",
"arxiv_id": "quant-ph/0511166",
"authors": [
"William Gordon Ritter"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.72.062328",
"journal_ref": "Phys. Rev. A 72, 062328 (2005)",
"title": "On the number of representations providing noiseless subsystems",
"url": "https://arxiv.org/abs/quant-ph/0511166"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "88da89f4-2283-4f63-8e6d-0f9e126a45e3",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}