Physics – Quantum Physics
Scientific paper
2007-12-12
Phys. Rev. A 78, 042303 (2008)
Physics
Quantum Physics
Version 4 is almost exactly the same as the published version in Phys. Rev. A
Scientific paper
10.1103/PhysRevA.78.042303
Graph states are generalized from qubits to collections of $n$ qudits of arbitrary dimension $D$, and simple graphical methods are used to construct both additive and nonadditive quantum error correcting codes. Codes of distance 2 saturating the quantum Singleton bound for arbitrarily large $n$ and $D$ are constructed using simple graphs, except when $n$ is odd and $D$ is even. Computer searches have produced a number of codes with distances 3 and 4, some previously known and some new. The concept of a stabilizer is extended to general $D$, and shown to provide a dual representation of an additive graph code.
Gheorghiu Vlad
Griffiths Robert B.
Looi Shiang Yong
Yu Li
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