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

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

2011-07-09

arxiv.org/abs/1107.1761v1

Phys. Rev. A 84, 052306 (2011)

Physics

Quantum Physics

15 pages, 2 figures

Scientific paper

10.1103/PhysRevA.84.052306

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.

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