  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.
