AT&T Weekly Seminar on Quantum Computing and Quantum Error Correction


QUANTUM COMPUTATION
AND
QUANTUM ERROR CORRECTION

Title:

Bounds for quantum codes Part II: Quantum Weight Enumerators

Speaker:

Eric Rains
AT&T

Place:

AT&T Laboratories
600 Mountain Avenue
Murray Hill, NJ
Murray Hill Building, Room: 2D-101

Time:

2:00 p.m.
Wednesday, February 12, 1997
Thanks to everyone for registering early AND arriving early.

ABSTRACT:

In part I, I described the linear programming bound for additive codes. It turns out that this bound can be extended to general codes, as I will be describing in part II. As the fundamental objects in the additive LP bound are the weight enumerators associated to a code, so in the general case, we need analogues of weight enumerators for general codes. This role is played, as we will see, by the Shor-Laflamme enumerators and the quantum shadow enumerator. With this, we get a bound for general codes very nearly as strong as the bounds for additive codes.

Additional references for part II:

"Quantum analog of the MacWilliams identities in classical coding theory" P. W. Shor and R. Laflamme LANL e-print quant-ph/9610040

This extends much of the additive LP bound to nonadditive codes.

"Quantum shadow enumerators" E. M. Rains LANL e-print quant-ph/9611001

And this extends the rest of the LP bound.

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Document last modified on January 31, 1997