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Published July 1998 | Submitted + Published
Journal Article Open

Quantum weight enumerators

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.

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.

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