dorsal/arxiv
View SchemaQuantum shadow enumerators
| Authors | E. M. Rains |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9611001 |
| URL | https://arxiv.org/abs/quant-ph/9611001 |
| Journal | IEEE Trans.Info.Theor. 45 (1999) 2361-2366 |
Abstract
In a recent paper [quant-ph/9610040], Shor and Laflamme define two ``weight enumerators'' for quantum error correcting codes, connected by a MacWilliams transform, and use them to give a linear-programming bound for quantum codes. We extend their work by introducing another enumerator, based on the classical theory of shadow codes, that tightens their bounds significantly. In particular, nearly all of the codes known to be optimal among additive quantum codes (codes derived from orthogonal geometry ([quant-ph/9608006])) can be shown to be optimal among all quantum codes. We also use the shadow machinery to extend a bound on additive codes (E. M. Rains, manuscript in preparation) to general codes, obtaining as a consequence that any code of length n can correct at most floor((n+1)/6) errors.
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"abstract": "In a recent paper [quant-ph/9610040], Shor and Laflamme define two ``weight\nenumerators\u0027\u0027 for quantum error correcting codes, connected by a MacWilliams\ntransform, and use them to give a linear-programming bound for quantum codes.\nWe extend their work by introducing another enumerator, based on the classical\ntheory of shadow codes, that tightens their bounds significantly. In\nparticular, nearly all of the codes known to be optimal among additive quantum\ncodes (codes derived from orthogonal geometry ([quant-ph/9608006])) can be\nshown to be optimal among all quantum codes. We also use the shadow machinery\nto extend a bound on additive codes (E. M. Rains, manuscript in preparation) to\ngeneral codes, obtaining as a consequence that any code of length n can correct\nat most floor((n+1)/6) errors.",
"arxiv_id": "quant-ph/9611001",
"authors": [
"E. M. Rains"
],
"categories": [
"quant-ph"
],
"journal_ref": "IEEE Trans.Info.Theor. 45 (1999) 2361-2366",
"title": "Quantum shadow enumerators",
"url": "https://arxiv.org/abs/quant-ph/9611001"
},
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