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

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. \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.

15 pages, 2 figures

References in corpus (7)

• Multi-party entanglement in graph states
• Codeword Stabilized Quantum Codes
• Quantum Error Correcting Codes Using Qudit Graph States
• Quantum Error Correction of Observables
• Framework for classifying logical operators in stabilizer codes
• Location of quantum information in additive graph codes
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• Small quantum networks in the qudit stabilizer formalism
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• Qudit Noisy Stabilizer Formalism