We show how to convert a quantum stabilizer code to a one- 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.

03.67.Mn Entanglement measures, witnesses, and other characterizations

03.67.Hk Quantum communication

68P30 Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) (See also 94Axx)

81P68 Quantum computation and quantum cryptography (See also 68Q05, 94A60)

94A15 Information theory, general (See also 62B10)

68M12 Network protocols

Computational physics

Quantum information and quantum mechanics

Issue 29 (25 July 2003)

Received 4 April 2003

Published 8 July 2003