dorsal/arxiv
View SchemaDecomposition of pure states of a quantum register
| Authors | Ioannis Raptis, Roman R. Zapatrin |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0010104 |
| URL | https://arxiv.org/abs/quant-ph/0010104 |
Abstract
Using the leading vector method, we show that any vector $h\in(C^2)^{\otimes l}$ can be decomposed as a sum of at most (and at least in the generic case) $2^l-l$ product vectors using local bitwise unitary transformations. The method is based on representing the vectors by chains of appropriate simplicial complex. This generalizes the Scmidt decomposition of pure states of a 2-bit register to registers of arbitrary length $l$.
{
"annotation_id": "52ab8e07-1f7b-4476-bdd3-64658d651faf",
"date_created": "2026-03-02T18:01:42.379000Z",
"date_modified": "2026-03-02T18:01:42.379000Z",
"file_hash": "4ee9f2ada8f3b2b7169e50074690e5f21ad39a239093d4e7fb299a2b57e6f819",
"private": false,
"record": {
"abstract": "Using the leading vector method, we show that any vector $h\\in(C^2)^{\\otimes\nl}$ can be decomposed as a sum of at most (and at least in the generic case)\n$2^l-l$ product vectors using local bitwise unitary transformations. The method\nis based on representing the vectors by chains of appropriate simplicial\ncomplex. This generalizes the Scmidt decomposition of pure states of a 2-bit\nregister to registers of arbitrary length $l$.",
"arxiv_id": "quant-ph/0010104",
"authors": [
"Ioannis Raptis",
"Roman R. Zapatrin"
],
"categories": [
"quant-ph",
"math.RA"
],
"title": "Decomposition of pure states of a quantum register",
"url": "https://arxiv.org/abs/quant-ph/0010104"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "0f8a9d63-b590-4bea-9e4c-30823ff80bb9",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}