Introduction

In EPR schemes, applying the reduction postulate projects the second particle instantaneously onto an eigenstate corresponding to the same quantization axis as the first measurement. If it were possible to determine this state completely, superluminal communication would become accessible: from this state, the second experimenter could calculate the direction of the quantization axis to which it corresponds, and rapidly know what direction was chosen by the first experimenter, even if the experimenters are in two different and remote galaxies. This, obviously, could be used as a sort of telegraph, completely free of any relativistic minimum delay (proportional to the distance covered) for the transmission of information. Nevertheless, we have seen in §7.2.1 that it is impossible to obtain a complete determination of a quantum state from a single realization of this state. Such a realization allows only one single measurement, which (almost always) perturbs the state, so that a second measurement on the same state is not feasible; there is not, and by far, sufficient information in the first measurement for a full determination of the quantum state – see discussion in §7.2. This telegraph would therefore not function.

If a single particle is not sufficient for Bob to get a message, could he use more particles? Suppose for a moment that a perfect “cloning” of quantum states could be performed – more precisely the reproduction with many particles of the unknown state of a single particle.