dorsal/arxiv
View SchemaQuantum Error Correcting Codes From The Compression Formalism
| Authors | Man-Duen Choi, David W. Kribs, Karol Zyczkowski |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0511101 |
| URL | https://arxiv.org/abs/quant-ph/0511101 |
| DOI | 10.1016/S0034-4877(06)80041-8 |
| Journal | Rep. Math. Phys., 58 (2006), 77-91. |
Abstract
We solve the fundamental quantum error correction problem for bi-unitary channels on two-qubit Hilbert space. By solving an algebraic compression problem, we construct qubit codes for such channels on arbitrary dimension Hilbert space, and identify correctable codes for Pauli-error models not obtained by the stabilizer formalism. This is accomplished through an application of a new tool for error correction in quantum computing called the ``higher-rank numerical range''. We describe its basic properties and discuss possible further applications.
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"abstract": "We solve the fundamental quantum error correction problem for bi-unitary\nchannels on two-qubit Hilbert space. By solving an algebraic compression\nproblem, we construct qubit codes for such channels on arbitrary dimension\nHilbert space, and identify correctable codes for Pauli-error models not\nobtained by the stabilizer formalism. This is accomplished through an\napplication of a new tool for error correction in quantum computing called the\n``higher-rank numerical range\u0027\u0027. We describe its basic properties and discuss\npossible further applications.",
"arxiv_id": "quant-ph/0511101",
"authors": [
"Man-Duen Choi",
"David W. Kribs",
"Karol Zyczkowski"
],
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"quant-ph",
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],
"doi": "10.1016/S0034-4877(06)80041-8",
"journal_ref": "Rep. Math. Phys., 58 (2006), 77-91.",
"title": "Quantum Error Correcting Codes From The Compression Formalism",
"url": "https://arxiv.org/abs/quant-ph/0511101"
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