Recycling of quantum information: Multiple observations of quantum clocks

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.