Quantum entanglement between two far-away constituents of a composite system, when considered in conjunction with a measurement process on one of them, raises some serious problems due to the instantaneous reduction of the state of the other. In some sense one could state that an action performed in a given space time region can affect immediately a system which is space like separated from it. It is not surprising that this peculiar aspect of quantum mechanics has given rise, from the seventies up to now, to many proposals to achieve superluminal communication between distant observers. Almost all such proposals have been shown to be wrong on the basis of general theorems by P. Eberhard and by our group. However, in 1982, a quite tricky new proposal has been put forward by N. Herbert whose refusal required the derivation of a new theorem, which has played and plays an important role for quantum computation and quantum communication: the no-cloning theorem. The seminar intends to briefly review the debate about this interesting issue which involves many subtle aspects of quantum mechanics and to make clear the events which led to the derivation of the no-cloning theorem. Finally, attention will be paid to the general problem of the compatibility of the reduction process "at-a-distance" and relativistic requirements, specifically in the light of the recent proposals of relativistic generalizations of "collapse theories".
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