Quantum MacWilliams Identities
Quantum Physics
2007-05-23 v1
Abstract
We derive a relationship between two different notions of fidelity (entanglement fidelity and average fidelity) for a completely depolarizing quantum channel. This relationship gives rise to a quantum analog of the MacWilliams identities in classical coding theory. These identities relate the weight enumerator of a code to the one of its dual and, with linear programming techniques, provided a powerful tool to investigate the possible existence of codes. The same techniques can be adapted to the quantum case. We give examples of their power.
Cite
@article{arxiv.quant-ph/9610040,
title = {Quantum MacWilliams Identities},
author = {Peter Shor and Raymond Laflamme},
journal= {arXiv preprint arXiv:quant-ph/9610040},
year = {2007}
}
Comments
3 pages in RevTex, the paper is also avalaible at http://qso.lanl.gov/qc/