Quantum Weight Enumerators

Details Quantum Weight Enumerators Quantum Weight Enumerators

1996-12-02

arxiv.org/abs/quant-ph/9612015v1

Physics

Quantum Physics

15 pages, AMSTeX, no figures

Scientific paper

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 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.

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