Degenerate quantum codes and the quantum Hamming bound
- Department of Physics and Astronomy, University of British Columbia, Vancouver V6T 1Z1 (Canada)
- Department of Computer Science, Texas A and M University, College Station, Texas 77843 (United States)
The parameters of a nondegenerate quantum code must obey the Hamming bound. An important open problem in quantum coding theory is whether the parameters of a degenerate quantum code can violate this bound for nondegenerate quantum codes. In this article we show that Calderbank-Shor-Steane (CSS) codes, over a prime power alphabet q{>=}5, cannot beat the quantum Hamming bound. We prove a quantum version of the Griesmer bound for the CSS codes, which allows us to strengthen the Rains' bound that an [[n,k,d]]{sub 2} code cannot correct more than [(n+1)/6] errors to [(n-k+1)/6]. Additionally, we also show that any [[n,k,d]]{sub q} quantum code with k+d{<=}(1-2eq{sup -2})n cannot beat the quantum Hamming bound.
- OSTI ID:
- 21413290
- Journal Information:
- Physical Review. A, Vol. 81, Issue 3; Other Information: DOI: 10.1103/PhysRevA.81.032318; (c) 2010 The American Physical Society; ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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