Reversing Measurement and Probabilistic Quantum Error Correction

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.