Maximal Holevo Quantity Based on Weak Measurements

The Holevo bound is a keystone in many applications of quantum information theory. We propose " maximal Holevo quantity for weak measurements" as the generalization of the maximal Holevo quantity which is defined by the optimal projective measurements. The scenarios that weak measurements is necessary are that only the weak measurements can be performed because for example the system is macroscopic or that one intentionally tries to do so such that the disturbance on the measured system can be controlled for example in quantum key distribution protocols. We evaluate systematically the maximal Holevo quantity for weak measurements for Bell-diagonal states and find a series of results. Furthermore, we find that weak measurements can be realized by noise and project measurements.