Improving information/disturbance and estimation/distortion trade-offs with non universal protocols by linear optics

We analyse in detail a conditional measurement scheme based on linear optical components, feed-forward loop and homodyne detection. The scheme may be used to achieve two different tasks. On the one hand it allows the extraction of information with minimum disturbance about a set of coherent states. On the other hand, it represents a nondemolitive measurement scheme for the annihilation operator, i.e. an indirect measurement of the Q-function. We investigate the information/disturbance trade-off for state inference and introduce the estimation/distortion trade-off to assess estimation of the Q-function. For coherent states chosen from a Gaussian set, we evaluate both information/disturbance and estimation/distortion trade-offs and found that non-universal protocols may be optimized in order to achieve better performances than universal ones. For Fock number states we prove that universal protocols do not exist and evaluate the estimation/distortion trade-off for a thermal distribution.