How much information can be obtained by a quantum measurement?

How much information about an unknown quantum state can be obtained by a measurement? We propose a model independent answer: the information obtained is equal to the minimum entropy of the outputs of the measurement, where the minimum is taken over all measurements which measure the same ``property'' of the state. This minimization is necessary because the measurement outcomes can be redundant, and this redundancy must be eliminated. We show that this minimum entropy is less or equal than the von Neumann entropy of the unknown states. That is a measurement can extract at most one meaningful bit from every qubit carried by the unknown states.