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We propose first protocol for anonymous distribution of quantum information that can be used to implement either channel with anonymous sender or channel with anonymous receiver. Our protocol achieves anonymity and message secrecy with unconditional security. It uses classical anonymous transfer. It tolerates disruption of the protocol, but the number of disrupters must be limited by the quantum Gilbert-Varshamov bound. This bound can be exceeded provided a specific entanglement distillation procedure will be used. A different version of the protocol tolerates any number of disrupters, but is secure only when receiver does not actively cooperate with other corrupted participants. A simplified version of this protocol was experimentally realized for 5 participants, but with different motivation [see Zhao et al., 2004].