dorsal/arxiv
View SchemaFundamentals of quantum mutual entropy and capacity
| Authors | Masanori Ohya |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9806042 |
| URL | https://arxiv.org/abs/quant-ph/9806042 |
| Journal | OpenSyst.Info.Dyn.6:69-78,1999 |
Abstract
The study of mutual entropy (information) and capacity in classica l system was extensively done after Shannon by several authors like Kolmogor ov and Gelfand. In quantum systems, there have been several definitions of t he mutual entropy for classical input and quantum output. In 1983, the autho r defined the fully quantum mechanical mutual entropy by means of the relati ve entropy of Umegaki, and he extended it to general quantum systems by the relative entropy of Araki and Uhlmann. When the author introduced the quantu m mutual entropy, he did not indicate that it contains other definitions of the mutual entropy including classical one, so that there exist several misu nderstandings for the use of the mutual entropy (information) to compute the capacity of quantum channels. Therefore in this note we point out that our quantum mutual entropy generalizes others and where the m isuse occurs.
{
"annotation_id": "4e3a1fde-fbbc-465b-86f1-7657b607b18b",
"date_created": "2026-03-02T18:02:43.880000Z",
"date_modified": "2026-03-02T18:02:43.880000Z",
"file_hash": "d44e1acf24ba53784be74c2f89d17274189e7e98dcb334074921367d4306caaf",
"private": false,
"record": {
"abstract": "The study of mutual entropy (information) and capacity in classica l system\nwas extensively done after Shannon by several authors like Kolmogor ov and\nGelfand. In quantum systems, there have been several definitions of t he mutual\nentropy for classical input and quantum output. In 1983, the autho r defined\nthe fully quantum mechanical mutual entropy by means of the relati ve entropy\nof Umegaki, and he extended it to general quantum systems by the relative\nentropy of Araki and Uhlmann. When the author introduced the quantu m mutual\nentropy, he did not indicate that it contains other definitions of the mutual\nentropy including classical one, so that there exist several misu nderstandings\nfor the use of the mutual entropy (information) to compute the capacity of\nquantum channels. Therefore in this note we point out that our quantum mutual\nentropy generalizes others and where the m isuse occurs.",
"arxiv_id": "quant-ph/9806042",
"authors": [
"Masanori Ohya"
],
"categories": [
"quant-ph"
],
"journal_ref": "OpenSyst.Info.Dyn.6:69-78,1999",
"title": "Fundamentals of quantum mutual entropy and capacity",
"url": "https://arxiv.org/abs/quant-ph/9806042"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "d44fd5e8-f99c-4f58-b2d4-f6bac69ecf51",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}