dorsal/arxiv
View SchemaTrade-off between the tolerance of located and unlocated errors in nondegenerate quantum error-correcting codes
| Authors | Henry L. Haselgrove, Peter P. Rohde |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0605183 |
| URL | https://arxiv.org/abs/quant-ph/0605183 |
| Journal | QIC 8, 0399 (2008) |
Abstract
In a recent study [Rohde et al., quant-ph/0603130 (2006)] of several quantum error correcting protocols designed for tolerance against qubit loss, it was shown that these protocols have the undesirable effect of magnifying the effects of depolarization noise. This raises the question of which general properties of quantum error-correcting codes might explain such an apparent trade-off between tolerance to located and unlocated error types. We extend the counting argument behind the well-known quantum Hamming bound to derive a bound on the weights of combinations of located and unlocated errors which are correctable by nondegenerate quantum codes. Numerical results show that the bound gives an excellent prediction to which combinations of unlocated and located errors can be corrected with high probability by certain large degenerate codes. The numerical results are explained partly by showing that the generalized bound, like the original, is closely connected to the information-theoretic quantity the quantum coherent information. However, we also show that as a measure of the exact performance of quantum codes, our generalized Hamming bound is provably far from tight.
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"abstract": "In a recent study [Rohde et al., quant-ph/0603130 (2006)] of several quantum\nerror correcting protocols designed for tolerance against qubit loss, it was\nshown that these protocols have the undesirable effect of magnifying the\neffects of depolarization noise. This raises the question of which general\nproperties of quantum error-correcting codes might explain such an apparent\ntrade-off between tolerance to located and unlocated error types. We extend the\ncounting argument behind the well-known quantum Hamming bound to derive a bound\non the weights of combinations of located and unlocated errors which are\ncorrectable by nondegenerate quantum codes. Numerical results show that the\nbound gives an excellent prediction to which combinations of unlocated and\nlocated errors can be corrected with high probability by certain large\ndegenerate codes. The numerical results are explained partly by showing that\nthe generalized bound, like the original, is closely connected to the\ninformation-theoretic quantity the quantum coherent information. However, we\nalso show that as a measure of the exact performance of quantum codes, our\ngeneralized Hamming bound is provably far from tight.",
"arxiv_id": "quant-ph/0605183",
"authors": [
"Henry L. Haselgrove",
"Peter P. Rohde"
],
"categories": [
"quant-ph"
],
"journal_ref": "QIC 8, 0399 (2008)",
"title": "Trade-off between the tolerance of located and unlocated errors in nondegenerate quantum error-correcting codes",
"url": "https://arxiv.org/abs/quant-ph/0605183"
},
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