Information gain and approximate reversibility of quantum measurements

We describe the information balance in a quantum measurements process. Our approach is completely general, and succeeds in providing, as a byproduct, a sound information- disturbance trade-off. In particular, we generalize the notion of coherent information from channels to quantum measurements, and show that such a quantity can accurately describe the disturbance that a quantum measurement unavoidably causes on the input system, whenever some useful information is extracted. The single-outcome case, that is, the case of measurements with post-selection, is finally discussed.