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Objectives. Quantum nonlocal correlations between random dissipative processes have both the retarded and advanced components. Experimental problem was to establish a correlation between a natural source-process and isolated from the classical local influences probe-process in the detector. Methods. In the mid-1990s, the first long-term experiment started with Troitsk lab setup. The second experiment has been running since 2012 at Baikal Deep Sea Neutrino Observatory. Due to the monogamy of quantum correlations, number of natural random dissipative processes causing a noticeable response of the detectors is small and predictable. Results. The experiments have shown that random component of solar activity is the dominant source. The global maximum of correlation with solar activity is at the advancement of order of 100 days and can be used for the forecast. We have calculated a number of long-term forecast series of random component of solar activity with a lead time of several months. Conclusion. Phenomenon of macroscopic nonlocality gives the unique possibility to forecast the random heliophysical processes.