  In this paper, we investigate the possibility of explaining nonclassical
correlations between two quantum systems in terms of quantum interferences
between collective states of the two systems. We achieve this by mapping the
relations between different measurement contexts in the product Hilbert space
of a pair of two-level systems onto an analogous sequence of interferences
between paths in a single-particle interferometer. The relations between
different measurement outcomes are then traced to the distribution of
probability currents in the interferometer, where paradoxical relations between
the outcomes are identified with currents connecting two states that are
orthogonal and should therefore exclude each other. We show that the relation
between probability currents and correlations can be represented by continuous
conditional (quasi)probability currents through the interferometer, given by
weak values; the violation of the noncontextual assumption is expressed by
negative conditional currents in some of the paths. Since negative conditional
currents correspond to the assignment of negative conditional probabilities to
measurements results in different measurement contexts, the necessity of such
negative probability currents represents a failure of noncontextual local
realism. Our results help to explain the meaning of nonlocal correlations in
quantum mechanics, and support Feynman's claim that interference is the origin
of all quantum phenomena.
