Codes for the quantum erasure channel

Abstract

The quantum erasure channel (QEC) is considered. Codes for the QEC have to correct for erasures, i.e., arbitrary errors at known positions. We show that four quantum bits are necessary and sufficient to encode one quantum bit and correct one erasure, in contrast to five quantum bits for unknown positions. Moreover, a family of quantum codes for the QEC, the quantum Bose-Chaudhuri-Hocquenghem codes, that can be efficiently decoded is introduced.