On a Problem Concerning the Quantum Hamming Bound for Impure Quantum Codes
Zhuo Li, Lijuan Xing · IEEE Transactions on Information Theory · 2010
A famous open problem in the theory of quantum error-correcting codes is whether or not the parameters of an impure quantum code can violate the quantum Hamming bound for pure quantum codes. We partially solve this problem. We demonstrate that there exists a thresholdN(d,m) such that an arbitrary((n,K,d))mquantum code must obey the quantum Hamming bound whenevern≥N(d,m). We list some values ofN(d,m) for smalldand binary quantum codes.