01361nas a2200157 4500008004100000245007900041210006900120260001200189520086500201100001801066700002201084700002401106700001701130700002101147856003501168 2007 eng d00aRecycling of quantum information: Multiple observations of quantum systems0 aRecycling of quantum information Multiple observations of quantu c08/20073 aGiven a finite number of copies of an unknown qubit state that have already been measured optimally, can one still extract any information about the original unknown state? We give a positive answer to this question and quantify the information obtainable by a given observer as a function of the number of copies in the ensemble, and of the number of independent observers that, one after the other, have independently measured the same ensemble of qubits before him. The optimality of the protocol is proven and extensions to other states and encodings are also studied. According to the general lore, the state after a measurement has no information about the state before the measurement. Our results manifestly show that this statement has to be taken with a grain of salt, specially in situations where the quantum states encode confidential information.1 aRapcan, Peter1 aCalsamiglia, John1 aMuñoz-Tapia, Ramon1 aBagan, Emili1 aBużek, Vladimir uhttp://arxiv.org/abs/0708.1086