Quantum weight enumerators

Rains, Eric M. (1998) Quantum weight enumerators. IEEE Transactions on Information Theory, 44 (4). pp. 1388-1394. ISSN 0018-9448. doi:10.1109/18.681316. https://resolver.caltech.edu/CaltechAUTHORS:20170925-154039545

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Abstract

In a recent paper, Shor and Laflamme (see Phys. Rev. Lett., vol.78, p.1600-2, 1997) defined two "weight enumerators" for quantum error-correcting codes, connected by a MacWilliams transform, and used them to give a linear programming bound for quantum codes. We introduce two new enumerators which, while much less powerful at producing bounds, are useful tools nonetheless. The new enumerators are connected by a much simpler duality transform, clarifying the duality between Shor and Laflamme's enumerators. We also use the new enumerators to give a simpler condition for a quantum code to have specified minimum distance, and to extend the enumerator theory to codes with block size greater than 2.

Item Type:

Article

Related URLs:

URL	URL Type	Description
https://doi.org/10.1109/18.681316	DOI	Article
http://ieeexplore.ieee.org/document/681316	Publisher	Article
https://arxiv.org/abs/quant-ph/9612015	arXiv	Discussion Paper

Additional Information:

© 1998 IEEE. Manuscript received December 20, 1996; revised December 31, 1997. The author wishes to thank P. Shor and N. Sloane for many helpful discussions; he would also like to thank C. Bennett for a helpful discussion on erasures.

Subject Keywords:

Weight enumerators q-ary quantum codes

Issue or Number:

DOI:

10.1109/18.681316

Record Number:

CaltechAUTHORS:20170925-154039545

Persistent URL:

https://resolver.caltech.edu/CaltechAUTHORS:20170925-154039545

Official Citation:

E. M. Rains, "Quantum weight enumerators," in IEEE Transactions on Information Theory, vol. 44, no. 4, pp. 1388-1394, Jul 1998. doi: 10.1109/18.681316 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=681316&isnumber=14976

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ID Code:

81818

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CaltechAUTHORS

Deposited By:

Tony Diaz

Deposited On:

25 Sep 2017 22:44

Last Modified:

15 Nov 2021 19:46

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