dorsal/arxiv
View SchemaA tight lower bound on the classical communication cost of entanglement dilution
| Authors | Aram Harrow, Hoi-Kwong Lo |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0204096 |
| URL | https://arxiv.org/abs/quant-ph/0204096 |
| Journal | IEEE Trans. Inf. Theory, Vol. 50, No. 2, (2004) p.319-327 |
Abstract
Entanglement concentration requires no classical communication, but the best prior art result for diluting to N copies of a partially entangled state requires an amount of communication on the order of sqrt(N) bits. Our main result is to prove this prior art result optimal up to a constant factor; any procedure for creating N partially entangled states from singlets requires Omega(sqrt(N)) bits of classical communication. Previously not even a constant bound was known for approximate entanglement transforms. We also prove a lower bound on the inefficiency of the process: to dilute singlets to N copies of a partially entangled state, the entropy of entanglement must decrease by Omega(sqrt(N)).
{
"annotation_id": "8d69a7d2-f1ec-4469-a97e-2d4f15a5868c",
"date_created": "2026-03-02T18:01:49.159000Z",
"date_modified": "2026-03-02T18:01:49.159000Z",
"file_hash": "563ba57a2eff2b251a6654d66b6e581a25a20447f1227c2c58a57f9d7760d2ae",
"private": false,
"record": {
"abstract": "Entanglement concentration requires no classical communication, but the best\nprior art result for diluting to N copies of a partially entangled state\nrequires an amount of communication on the order of sqrt(N) bits. Our main\nresult is to prove this prior art result optimal up to a constant factor; any\nprocedure for creating N partially entangled states from singlets requires\nOmega(sqrt(N)) bits of classical communication. Previously not even a constant\nbound was known for approximate entanglement transforms.\n We also prove a lower bound on the inefficiency of the process: to dilute\nsinglets to N copies of a partially entangled state, the entropy of\nentanglement must decrease by Omega(sqrt(N)).",
"arxiv_id": "quant-ph/0204096",
"authors": [
"Aram Harrow",
"Hoi-Kwong Lo"
],
"categories": [
"quant-ph"
],
"journal_ref": "IEEE Trans. Inf. Theory, Vol. 50, No. 2, (2004) p.319-327",
"title": "A tight lower bound on the classical communication cost of entanglement dilution",
"url": "https://arxiv.org/abs/quant-ph/0204096"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "550a310b-07c1-4c3a-90f3-d9c11c584f2f",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}