Information capacity of a quantum observable

In this paper we consider the classical capacities of quantum-classical channels corresponding to measurement of observables. Special attention is paid to the case of continuous observables. We give formulas for unassisted and entanglement-assisted classical capacities C and C (ea) and consider some explicitly solvable cases, which give simple examples of entanglement-breaking channels with C < C (ea). We also elaborate on the ensemble-observable duality to show that C (ea) for the measurement channel is related to the chi-quantity for the dual ensemble in the same way as C is related to the accessible information. This provides both accessible information and the chi-quantity for quantum ensembles dual to our examples.