Tripartite Entanglement in Qudit Stabilizer States and Application in Quantum Error Correction

2011/07/09 by Shiang Yong Looi, Robert B. Griffiths · 2 citations
Physics and Astronomy · #quant-ph

paper · pdf · doi:10.1103/physreva.84.052306

published as Phys. Rev. A 84, 052306 (2011) · 15 pages, 2 figures

arxiv created 2011/07/09 · arxiv updated 2011/12/05

Abstract

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. 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.

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