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Entanglement Purification of Any Stabilizer State

Published

Author(s)

Scott Glancy, Emanuel Knill, Hilma M. Vasconcelos

Abstract

We present a method for multipartite entanglement purification of any stabilizer state shared by several parties. In our protocol each party measures the stabilizer operators of a quantum error correcting code on his or her qubits. The parties exchange their syndrome results, detect or correct errors and decode the desired purified state. We give necessary and sufficient conditions on the stabilizer codes which may be used in this procedure and find that the Steane seven qubit code is the smallest error correcting code sufficient to purify any stabilizer state. An error detecting code which encodes two qubits in six can also be used to purify an stabilizer state. We further specify what classes of stabilizer codes can purify what classes of stabilizer states.
Citation
Physical Review A (Atomic, Molecular and Optical Physics)
Volume
74

Keywords

entanglement distillation, entanglement purification, quantum error correction, stabilizer codes.

Citation

Glancy, S. , Knill, E. and Vasconcelos, H. (2006), Entanglement Purification of Any Stabilizer State, Physical Review A (Atomic, Molecular and Optical Physics), [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=150365 (Accessed February 26, 2024)
Created December 31, 2005, Updated October 12, 2021