dorsal/arxiv
View SchemaLower Bounds on the Quantum Capacity and Highest Error Exponent of General Memoryless Channels
| Authors | Mitsuru Hamada |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0112103 |
| URL | https://arxiv.org/abs/quant-ph/0112103 |
| DOI | 10.1109/TIT.2002.801470 |
| Journal | IEEE Trans. Information Theory, vol.48, no.9, pp.2547--2557, Sept. 2002 |
Abstract
Tradeoffs between the information rate and fidelity of quantum error-correcting codes are discussed. Quantum channels to be considered are those subject to independent errors and modeled as tensor products of copies of a general completely positive linear map, where the dimension of the underlying Hilbert space is a prime number. On such a quantum channel, the highest fidelity of a quantum error-correcting code 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). The E(R) is positive below some threshold R', which implies R' is a lower bound on the quantum capacity. The result of this work applies to general discrete memoryless channels, including channel models derived from a physical law of time evolution, or from master equations.
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"abstract": "Tradeoffs between the information rate and fidelity of quantum\nerror-correcting codes are discussed. Quantum channels to be considered are\nthose subject to independent errors and modeled as tensor products of copies of\na general completely positive linear map, where the dimension of the underlying\nHilbert space is a prime number. On such a quantum channel, the highest\nfidelity of a quantum error-correcting code of length $n$ and rate R is proven\nto be lower bounded by 1 - \\exp [-n E(R) + o(n)] for some function E(R). The\nE(R) is positive below some threshold R\u0027, which implies R\u0027 is a lower bound on\nthe quantum capacity. The result of this work applies to general discrete\nmemoryless channels, including channel models derived from a physical law of\ntime evolution, or from master equations.",
"arxiv_id": "quant-ph/0112103",
"authors": [
"Mitsuru Hamada"
],
"categories": [
"quant-ph"
],
"doi": "10.1109/TIT.2002.801470",
"journal_ref": "IEEE Trans. Information Theory, vol.48, no.9, pp.2547--2557, Sept.\n 2002",
"title": "Lower Bounds on the Quantum Capacity and Highest Error Exponent of General Memoryless Channels",
"url": "https://arxiv.org/abs/quant-ph/0112103"
},
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