Quantum witness and invasiveness of cosmic neutrino measurements

Measurements of cosmic neutrinos have a reach potential for providing an insight into fundamental neutrino properties. For this a precise knowledge about an astrophysical environment of cosmic neutrinos propagation is needed. However this is not always possible, and the lack of information can bring about theoretical uncertainties in our physical interpretation of the results of experiments on cosmic neutrino fluxes. We formulate an approach that allows one to quantify the uncertainties using the apparatus of quantum measurement theory. We consider high-energy Dirac neutrinos emitted by some distant source and propagating towards the earth in the interstellar space. It is supposed that neutrinos can meet on their way to the detector at the earth a dense cosmic object serving as a filter that stops active, left-handed neutrinos and letting only sterile, right-handed neutrinos to propagate further. Such a filter mimics the strongest effect on the neutrino flux that can be induced by the cosmic object and that can be missed in the theoretical interpretation of the lab measurements due to the insufficient information about the astrophysical environment of the neutrino propagation. Treating the neutrino interaction with the cosmic object as the first, neutrino-spin measurement, whose result is not recorded, we study its invasive effect on the second, neutrino-flavor measurement in the lab.