dorsal/arxiv
View SchemaEntanglement of Assistance is not a bipartite measure nor a tripartite monotone
| Authors | Gilad Gour, Robert W. Spekkens |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0512139 |
| URL | https://arxiv.org/abs/quant-ph/0512139 |
| DOI | 10.1103/PhysRevA.73.062331 |
| Journal | Phys. Rev. A 73, 062331 (2006) |
Abstract
The entanglement of assistance quantifies the entanglement that can be generated between two parties, Alice and Bob, given assistance from a third party, Charlie, when the three share a tripartite state and where the assistance consists of Charlie initially performing a measurement on his share and communicating the result to Alice and Bob through a one-way classical channel. We argue that if this quantity is to be considered an operational measure of entanglement, then it must be understood to be a tripartite rather than a bipartite measure. We compare it with a distinct tripartite measure that quantifies the entanglement that can be generated between Alice and Bob when they are allowed to make use of a two-way classical channel with Charlie. We show that the latter quantity, which we call the entanglement of collaboration, can be greater than the entanglement of assistance. This demonstrates that the entanglement of assistance (considered as a tripartite measure of entanglement), and its multipartite generalizations such as the localizable entanglement, are not entanglement monotones, thereby undermining their operational significance.
{
"annotation_id": "44d1e9a7-f113-4a0b-9163-7997291c4c8a",
"date_created": "2026-03-02T18:02:24.066000Z",
"date_modified": "2026-03-02T18:02:24.066000Z",
"file_hash": "49d86b39d62189f78192994e17ab0e6954a6058b6fbf97c541fc114176b48556",
"private": false,
"record": {
"abstract": "The entanglement of assistance quantifies the entanglement that can be\ngenerated between two parties, Alice and Bob, given assistance from a third\nparty, Charlie, when the three share a tripartite state and where the\nassistance consists of Charlie initially performing a measurement on his share\nand communicating the result to Alice and Bob through a one-way classical\nchannel. We argue that if this quantity is to be considered an operational\nmeasure of entanglement, then it must be understood to be a tripartite rather\nthan a bipartite measure. We compare it with a distinct tripartite measure that\nquantifies the entanglement that can be generated between Alice and Bob when\nthey are allowed to make use of a two-way classical channel with Charlie. We\nshow that the latter quantity, which we call the entanglement of collaboration,\ncan be greater than the entanglement of assistance. This demonstrates that the\nentanglement of assistance (considered as a tripartite measure of\nentanglement), and its multipartite generalizations such as the localizable\nentanglement, are not entanglement monotones, thereby undermining their\noperational significance.",
"arxiv_id": "quant-ph/0512139",
"authors": [
"Gilad Gour",
"Robert W. Spekkens"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.73.062331",
"journal_ref": "Phys. Rev. A 73, 062331 (2006)",
"title": "Entanglement of Assistance is not a bipartite measure nor a tripartite monotone",
"url": "https://arxiv.org/abs/quant-ph/0512139"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "56beb0c0-d438-4951-a418-4c76ed3bcd85",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}