dorsal/arxiv
View SchemaAspects of generic entanglement
| Authors | Patrick Hayden, Debbie W. Leung, Andreas Winter |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0407049 |
| URL | https://arxiv.org/abs/quant-ph/0407049 |
| DOI | 10.1007/s00220-006-1535-6 |
| Journal | Comm. Math. Phys. Vol. 265, No. 1, pp. 95-117, 2006. |
Abstract
We study entanglement and other correlation properties of random states in high-dimensional bipartite systems. These correlations are quantified by parameters that are subject to the "concentration of measure" phenomenon, meaning that on a large-probability set these parameters are close to their expectation. For the entropy of entanglement, this has the counterintuitive consequence that there exist large subspaces in which all pure states are close to maximally entangled. This, in turn, implies the existence of mixed states with entanglement of formation near that of a maximally entangled state, but with negligible quantum mutual information and, therefore, negligible distillable entanglement, secret key, and common randomness. It also implies a very strong locking effect for the entanglement of formation: its value can jump from maximal to near zero by tracing over a number of qubits negligible compared to the size of total system. Furthermore, such properties are generic. Similar phenomena are observed for random multiparty states, leading us to speculate on the possibility that the theory of entanglement is much simplified when restricted to asymptotically generic states. Further consequences of our results include a complete derandomization of the protocol for universal superdense coding of quantum states.
{
"annotation_id": "5712841d-721f-42a1-a9a0-384c27b4da72",
"date_created": "2026-03-02T18:02:10.289000Z",
"date_modified": "2026-03-02T18:02:10.289000Z",
"file_hash": "20f01a7039d99715b5785ea212e51caa34f852e35e5f57b15e84060085e3db1f",
"private": false,
"record": {
"abstract": "We study entanglement and other correlation properties of random states in\nhigh-dimensional bipartite systems. These correlations are quantified by\nparameters that are subject to the \"concentration of measure\" phenomenon,\nmeaning that on a large-probability set these parameters are close to their\nexpectation. For the entropy of entanglement, this has the counterintuitive\nconsequence that there exist large subspaces in which all pure states are close\nto maximally entangled. This, in turn, implies the existence of mixed states\nwith entanglement of formation near that of a maximally entangled state, but\nwith negligible quantum mutual information and, therefore, negligible\ndistillable entanglement, secret key, and common randomness. It also implies a\nvery strong locking effect for the entanglement of formation: its value can\njump from maximal to near zero by tracing over a number of qubits negligible\ncompared to the size of total system. Furthermore, such properties are generic.\nSimilar phenomena are observed for random multiparty states, leading us to\nspeculate on the possibility that the theory of entanglement is much simplified\nwhen restricted to asymptotically generic states. Further consequences of our\nresults include a complete derandomization of the protocol for universal\nsuperdense coding of quantum states.",
"arxiv_id": "quant-ph/0407049",
"authors": [
"Patrick Hayden",
"Debbie W. Leung",
"Andreas Winter"
],
"categories": [
"quant-ph"
],
"doi": "10.1007/s00220-006-1535-6",
"journal_ref": "Comm. Math. Phys. Vol. 265, No. 1, pp. 95-117, 2006.",
"title": "Aspects of generic entanglement",
"url": "https://arxiv.org/abs/quant-ph/0407049"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "bc1c287f-85fe-4a0f-a164-9f8b21187c31",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}