dorsal/arxiv
View SchemaAn Ergodic Theorem for the Quantum Relative Entropy
| Authors | Igor Bjelakovic, Rainer Siegmund-Schultze |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0306094 |
| URL | https://arxiv.org/abs/quant-ph/0306094 |
| DOI | 10.1007/s00220-004-1054-2 |
Abstract
We prove the ergodic version of the quantum Stein's lemma which was conjectured by Hiai and Petz. The result provides an operational and statistical interpretation of the quantum relative entropy as a statistical measure of distinguishability, and contains as a special case the quantum version of the Shannon-McMillan theorem for ergodic states. A version of the quantum relative Asymptotic Equipartition Property (AEP) is given.
{
"annotation_id": "78b01b2f-18fd-480f-a02d-264497b54310",
"date_created": "2026-03-02T18:02:00.292000Z",
"date_modified": "2026-03-02T18:02:00.292000Z",
"file_hash": "3c3e78ecbe3b14aa2909ac9eae23cd2ba4d70c831639ae29a1aefb04d88557e1",
"private": false,
"record": {
"abstract": "We prove the ergodic version of the quantum Stein\u0027s lemma which was\nconjectured by Hiai and Petz. The result provides an operational and\nstatistical interpretation of the quantum relative entropy as a statistical\nmeasure of distinguishability, and contains as a special case the quantum\nversion of the Shannon-McMillan theorem for ergodic states. A version of the\nquantum relative Asymptotic Equipartition Property (AEP) is given.",
"arxiv_id": "quant-ph/0306094",
"authors": [
"Igor Bjelakovic",
"Rainer Siegmund-Schultze"
],
"categories": [
"quant-ph",
"math-ph",
"math.MP",
"math.PR"
],
"doi": "10.1007/s00220-004-1054-2",
"title": "An Ergodic Theorem for the Quantum Relative Entropy",
"url": "https://arxiv.org/abs/quant-ph/0306094"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "706839ae-dfaf-4b4e-ab24-237bc2744af6",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}