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In recent decades it was established that the quantum measurements of physical quantities in space-time points divided by space-like intervals may be correlated. Though such correlation follows from the formulas of quantum mechanics its physics so far remains unclear and there is a number of different and rather contradictory interpretations. They concern particularly the so-called Einstein-Podolsky-Rosen paradox where the momentary action at a distance together with non-local entangled states is used for the interpretation. We assume that the quantum theory can be formulated as local and look for the consequences of this assumption. Accordingly we try to explain the correlation phenomena in a local way looking for the origin of correlation. To exclude a presupposed correlation of participating quantum particles we consider two independent particle sources and two detectors that are independent as well. We show that the origin of the correlation is the feature that the occupation number of a particle (and other its measurable quantities) is formed by a pair of complex conjugated wave functions with in general arbitrary phases. We consider this point as crucial as it provides interpretation of the observed correlation phenomena that may otherwise look puzzling. We briefly discuss a special type of noise that is typical for the quantum correlation phenomena.
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