How much information about the original state preparation can be extracted
from a quantum system which already has been measured? That is, how many
independent (non-communicating) observers can measure the quantum system
sequentially and give a nontrivial estimation of the original unknown state? We
investigate these questions and we show from a simple example that quantum
information is not entirely lost as a result of the measurement-induced
collapse of the quantum state, and that an infinite number of independent
observers who have no prior knowledge about the initial state can gain a
partial information about the original preparation of the quantum system.