dorsal/arxiv
View SchemaClassical Capacity of Quantum Binary Adder Channels
| Authors | Gleb V. Klimovitch, Andreas Winter |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0502055 |
| URL | https://arxiv.org/abs/quant-ph/0502055 |
Abstract
We analyze the quantum binary adder channel, i.e. the quantum generalization of the classical, and well-studied, binary adder channel: in this model qubits rather than classical bits are transmitted. This of course is as special case of the general theory of quantum multiple access channels, and we may apply the established formulas for the capacity region to it. However, the binary adder channel is of particular interest classically, which motivates our generalizing it to the quantum domain. It turns out to be a very nice case study not only of multi-user quantum information theory, but also on the role entanglement plays there. It turns out that the analogous classical situation, the multi-user channel supported by shared randomness, is not distinct from the channel without shared randomness, as far as rates are concerned. However, we discuss the effect the new resource has on error probabilities, in an appendix. We focus specially on the effect entanglement between the senders as well as between senders and receiver has on the capacity region. Interestingly, in some of these cases one can devise rather simple codes meeting the capacity bounds, even in a zero-error model, which is in marked difference to code construction in the classical case.
{
"annotation_id": "4191a2ce-351b-4c28-8dd8-821419ebb1a7",
"date_created": "2026-03-02T18:02:13.739000Z",
"date_modified": "2026-03-02T18:02:13.739000Z",
"file_hash": "64ecfe6904e13f7fdfec079a92e5717bfaaf13ecdee74d76aebbf7efed0f911d",
"private": false,
"record": {
"abstract": "We analyze the quantum binary adder channel, i.e. the quantum generalization\nof the classical, and well-studied, binary adder channel: in this model qubits\nrather than classical bits are transmitted. This of course is as special case\nof the general theory of quantum multiple access channels, and we may apply the\nestablished formulas for the capacity region to it. However, the binary adder\nchannel is of particular interest classically, which motivates our generalizing\nit to the quantum domain. It turns out to be a very nice case study not only of\nmulti-user quantum information theory, but also on the role entanglement plays\nthere. It turns out that the analogous classical situation, the multi-user\nchannel supported by shared randomness, is not distinct from the channel\nwithout shared randomness, as far as rates are concerned. However, we discuss\nthe effect the new resource has on error probabilities, in an appendix.\n We focus specially on the effect entanglement between the senders as well as\nbetween senders and receiver has on the capacity region. Interestingly, in some\nof these cases one can devise rather simple codes meeting the capacity bounds,\neven in a zero-error model, which is in marked difference to code construction\nin the classical case.",
"arxiv_id": "quant-ph/0502055",
"authors": [
"Gleb V. Klimovitch",
"Andreas Winter"
],
"categories": [
"quant-ph"
],
"title": "Classical Capacity of Quantum Binary Adder Channels",
"url": "https://arxiv.org/abs/quant-ph/0502055"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "7e5beb21-cbe4-410b-9514-06aa04a5b966",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}