  The present paper is devoted to investigation of the entropy reduction and
entanglement-assisted classical capacity (information gain) of continuous
variable quantum measurements. These quantities are computed explicitly for
multimode Gaussian measurement channels. For this we establish a fundamental
property of the entropy reduction of a measurement: under a restriction on the
second moments of the input state it is maximized by a Gaussian state
(providing an analytical expression for the maximum). In the case of one mode,
the gain of entanglement assistance is investigated in detail.
