Conversion of a general quantum stabilizer code to an entanglement distillation protocol

Abstract

We show how to convert a quantum stabilizer code to a one-way or two-way entanglement distillation protocol. The proposed conversion method is a generalization of those of Shor-Preskill and Nielsen-Chuang. The recurrence protocol and the quantum privacy amplification protocol are equivalent to the protocols converted from [[2,1]] stabilizer codes. We also give an example of a two-way protocol converted from a stabilizer better than the recurrence protocol and the quantum privacy amplification protocol. The distillable entanglement by the class of one-way protocols converted from stabilizer codes for a certain class of states is equal to or greater than the achievable rate of stabilizer codes over the channel corresponding to the distilled state, and they can distill asymptotically more entanglement from a very noisy Werner state than the hashing protocol.Comment: LaTeX2e, 18 pages, 1 figure. Version 4 added an example of two-way protocols better than the recurrence protocol and the quantum privacy amplification protocol. Version 2 added the quantum privacy amplification protocol as an example converted from a stabilizer code, and corrected many errors. Results unchanged from V