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Is it possible to entangle two particles so that when one of them is measured, somehow, that can be detected by the other particle? No matter whether or not it is necessary to measure the second particle, or if it is necessary to measure any other related magnitude.

Vicent
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No. If one of the particles lies outside the lightcone of the other when the measurement is performed, no information regarding the measurement can leak to that region of space-time. The idea behind entanglement is that performing the measurement and knowing that the composite state is entangled (i.e, knowing about its preparation) gives the observer knowledge of the other particles' state. That is the reason why entanglement physics does not violate causality (well, and the idea that measurements are enacted by local operators, which opens the question of how locality is ultimately built in general quantum systems).