We consider a probabilistic reversing operation that returns the measured system to its original state by means of a physical process, and derive a trade-off relation between the unsharpness of the measurement and the best efficiency of the reversing operation. Such a reversing operation is shown to serve as a probabilistic quantum error correction, which will be useful when the numbers of qubits and gate operations are limited.

• Received 24 March 1998

DOI:https://doi.org/10.1103/PhysRevLett.82.2598