dorsal/arxiv
View SchemaA Lower Bound on the Quantum Capacity of Channels with Correlated Errors
| Authors | Mitsuru Hamada |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0201056 |
| URL | https://arxiv.org/abs/quant-ph/0201056 |
| DOI | 10.1063/1.1495537 |
| Journal | Journal of Mathematical Physics, vol.43, no.9, pp.4382--4390, Sept. 2002 |
Abstract
The highest fidelity of quantum error-correcting codes of length n and rate R is proven to be lower bounded by 1 - exp [-n E(R)+ o(n)] for some function E(R) on noisy quantum channels that are subject to not necessarily independent errors. The E(R) is positive below some threshold R', which implies R' is a lower bound on the quantum capacity. This work is an extension of the author's previous works [M. Hamada, Phys. Rev. A, 65, 052305, 2002 (e-Print quant-ph/0109114, LANL, 2001), and M. Hamada, submitted to IEEE Trans. Inf. Theory, 2002 (e-Print quant-ph/0112103, LANL, 2001)], which presented the bound for channels subject to independent errors, or channels modeled as tensor products of copies of a completely positive linear map. The relation of the channel class treated in this paper to those in the previous works are similar to that of Markov chains to sequences of independent identically distributed random variables.
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"abstract": "The highest fidelity of quantum error-correcting codes of length n and rate R\nis proven to be lower bounded by 1 - exp [-n E(R)+ o(n)] for some function E(R)\non noisy quantum channels that are subject to not necessarily independent\nerrors. The E(R) is positive below some threshold R\u0027, which implies R\u0027 is a\nlower bound on the quantum capacity. This work is an extension of the author\u0027s\nprevious works [M. Hamada, Phys. Rev. A, 65, 052305, 2002 (e-Print\nquant-ph/0109114, LANL, 2001), and M. Hamada, submitted to IEEE Trans. Inf.\nTheory, 2002 (e-Print quant-ph/0112103, LANL, 2001)], which presented the bound\nfor channels subject to independent errors, or channels modeled as tensor\nproducts of copies of a completely positive linear map. The relation of the\nchannel class treated in this paper to those in the previous works are similar\nto that of Markov chains to sequences of independent identically distributed\nrandom variables.",
"arxiv_id": "quant-ph/0201056",
"authors": [
"Mitsuru Hamada"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.1495537",
"journal_ref": "Journal of Mathematical Physics, vol.43, no.9, pp.4382--4390,\n Sept. 2002",
"title": "A Lower Bound on the Quantum Capacity of Channels with Correlated Errors",
"url": "https://arxiv.org/abs/quant-ph/0201056"
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