%0 Journal Article
%T Tripartite Entanglement in Qudit Stabilizer States and Application in Quantum Error Correction
%A Shiang Yong Looi
%A Robert B. Griffiths
%J Mathematics
%D 2011
%I arXiv
%R 10.1103/PhysRevA.84.052306
%X Consider a stabilizer state on $n$ qudits, each of dimension $D$ with $D$ being a prime or a squarefree integer, divided into three mutually disjoint sets or parts. Generalizing a result of Bravyi et al. [J. Math. Phys. \textbf{47}, 062106 (2006)] for qubits (D=2), we show that up to local unitaries on the three parts the state can be written as a tensor product of unentangled single-qudit states, maximally entangled EPR pairs, and tripartite GHZ states. We employ this result to obtain a complete characterization of the properties of a class of channels associated with stabilizer error-correcting codes, along with their complementary channels.
%U http://arxiv.org/abs/1107.1761v1