dorsal/arxiv
View SchemaCatalytic quantum error correction
| Authors | Todd Brun, Igor Devetak, Min-Hsiu Hsieh |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0608027 |
| URL | https://arxiv.org/abs/quant-ph/0608027 |
| DOI | 10.1109/TIT.2014.2313559 |
| Journal | IEEE Transactions on Information Theory 60, 3073 - 3089 (2014) |
Abstract
We develop the theory of entanglement-assisted quantum error correcting (EAQEC) codes, a generalization of the stabilizer formalism to the setting in which the sender and receiver have access to pre-shared entanglement. Conventional stabilizer codes are equivalent to dual-containing symplectic codes. In contrast, EAQEC codes do not require the dual-containing condition, which greatly simplifies their construction. We show how any quaternary classical code can be made into a EAQEC code. In particular, efficient modern codes, like LDPC codes, which attain the Shannon capacity, can be made into EAQEC codes attaining the hashing bound. In a quantum computation setting, EAQEC codes give rise to catalytic quantum codes which maintain a region of inherited noiseless qubits. We also give an alternative construction of EAQEC codes by making classical entanglement assisted codes coherent.
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"abstract": "We develop the theory of entanglement-assisted quantum error correcting\n(EAQEC) codes, a generalization of the stabilizer formalism to the setting in\nwhich the sender and receiver have access to pre-shared entanglement.\nConventional stabilizer codes are equivalent to dual-containing symplectic\ncodes. In contrast, EAQEC codes do not require the dual-containing condition,\nwhich greatly simplifies their construction. We show how any quaternary\nclassical code can be made into a EAQEC code. In particular, efficient modern\ncodes, like LDPC codes, which attain the Shannon capacity, can be made into\nEAQEC codes attaining the hashing bound. In a quantum computation setting,\nEAQEC codes give rise to catalytic quantum codes which maintain a region of\ninherited noiseless qubits.\n We also give an alternative construction of EAQEC codes by making classical\nentanglement assisted codes coherent.",
"arxiv_id": "quant-ph/0608027",
"authors": [
"Todd Brun",
"Igor Devetak",
"Min-Hsiu Hsieh"
],
"categories": [
"quant-ph"
],
"doi": "10.1109/TIT.2014.2313559",
"journal_ref": "IEEE Transactions on Information Theory 60, 3073 - 3089 (2014)",
"title": "Catalytic quantum error correction",
"url": "https://arxiv.org/abs/quant-ph/0608027"
},
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