How much information about the original state preparation can be extracted
from a quantum system which has already been measured? That is, how many in
dependent (noncommunicating) observers can measure the quantum system seque
ntially and give a nontrivial estimation of the original unknown state? We
investigate these questions, and show from a simple example that informatio
n about the original preparation is not entirely lost as a result of the me
asurement-induced collapse of the quantum state, and that an infinite numbe
r of independent observers who have no prior knowledge about the initial st
ate can gain partial information about the original preparation of the quan
tum system.