dorsal/arxiv
View SchemaOn environment-assisted capacities of quantum channels
| Authors | Andreas Winter |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0507045 |
| URL | https://arxiv.org/abs/quant-ph/0507045 |
| Journal | Markov Proc. Rel. Fields 13(1-2):297-314, 2007 |
Abstract
Following initial work by Gregoratti and Werner [J. Mod. Optics 50, 913-933, 2003 and quant-ph/0403092] and Hayden and King [quant-ph/0409026], we study the problem of the capacity of a quantum channel assisted by a "friendly (channel) environment" that can locally measure and communicate classical messages to the receiver. Previous work [quant-ph/0505038] has yielded a capacity formula for the quantum capacity under this kind of help from the environment. Here we study the problem of the environment-assisted classical capacity, which exhibits a somewhat richer structure (at least, it seems to be the harder problem). There are several, presumably inequivalent, models of the permitted local operations and classical communications between receiver and environment: one-way, arbitrary, separable and PPT POVMs. In all these models, the task of decoding a message amounts to discriminating a set of possibly entangled states between the two receivers, by a class of operations under some sort of locality constraint. After introducing the operational capacities outlined above, we show that a lower bound on the environment-assisted classical capacity is always half the logarithm of the input space dimension. Then we develop a few techniques to prove the existence of channels which meet this lower bound up to terms of much smaller order, even when PPT decoding measurements are allowed (assuming a certain superadditivity conjecture).
{
"annotation_id": "054e00c4-a27b-4618-beaf-b71895e529c5",
"date_created": "2026-03-02T18:02:17.254000Z",
"date_modified": "2026-03-02T18:02:17.254000Z",
"file_hash": "865fa3d70ee19a5ee8de3982fff76dda636a463f253683b288488efc72794542",
"private": false,
"record": {
"abstract": "Following initial work by Gregoratti and Werner [J. Mod. Optics 50, 913-933,\n2003 and quant-ph/0403092] and Hayden and King [quant-ph/0409026], we study the\nproblem of the capacity of a quantum channel assisted by a \"friendly (channel)\nenvironment\" that can locally measure and communicate classical messages to the\nreceiver.\n Previous work [quant-ph/0505038] has yielded a capacity formula for the\nquantum capacity under this kind of help from the environment. Here we study\nthe problem of the environment-assisted classical capacity, which exhibits a\nsomewhat richer structure (at least, it seems to be the harder problem). There\nare several, presumably inequivalent, models of the permitted local operations\nand classical communications between receiver and environment: one-way,\narbitrary, separable and PPT POVMs. In all these models, the task of decoding a\nmessage amounts to discriminating a set of possibly entangled states between\nthe two receivers, by a class of operations under some sort of locality\nconstraint.\n After introducing the operational capacities outlined above, we show that a\nlower bound on the environment-assisted classical capacity is always half the\nlogarithm of the input space dimension. Then we develop a few techniques to\nprove the existence of channels which meet this lower bound up to terms of much\nsmaller order, even when PPT decoding measurements are allowed (assuming a\ncertain superadditivity conjecture).",
"arxiv_id": "quant-ph/0507045",
"authors": [
"Andreas Winter"
],
"categories": [
"quant-ph"
],
"journal_ref": "Markov Proc. Rel. Fields 13(1-2):297-314, 2007",
"title": "On environment-assisted capacities of quantum channels",
"url": "https://arxiv.org/abs/quant-ph/0507045"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "63cdb24a-1c32-45d0-b7ad-a4a57df55322",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}