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- W2070290063 abstract "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 $qensuremath{geqslant}5$, 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 $[[n,k,d]{]}_{2}$ code cannot correct more than $ensuremath{lfloor}(n+1)/6ensuremath{rfloor}$ errors to $ensuremath{lfloor}(nensuremath{-}k+1)/6ensuremath{rfloor}$. Additionally, we also show that any $[[n,k,d]{]}_{q}$ quantum code with $k+densuremath{leqslant}(1ensuremath{-}2{mathit{eq}}^{ensuremath{-}2})n$ cannot beat the quantum Hamming bound." @default.
- W2070290063 created "2016-06-24" @default.
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- W2070290063 date "2010-03-19" @default.
- W2070290063 modified "2023-09-30" @default.
- W2070290063 title "Degenerate quantum codes and the quantum Hamming bound" @default.
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- W2070290063 doi "https://doi.org/10.1103/physreva.81.032318" @default.
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