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Quantum operations provide a general description of the state changes allowed by quantum mechanics. Simple necessary and sufficient conditions for an ideal quantum operation to be reversible by a unitary operation are derived in this paper. These results generalize recent work on reversible measurements by Mabuchi and Zoller Phys. Rev. Lett. 76, 3108 (1996). Quantum teleportation can be understood as a special case of the problem of reversing quantum operations. We characterize completely teleportation schemes of the type proposed by Bennett et al. Phys. Rev. Lett. 70, 1895 (1993).
Nielsen et al. (Tue,) studied this question.