Tracing quantum correlations back to collective interferences

Abstract

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.

Counterfactuality, back-action, and information gain in multi-path interferometers

“…Using the ideas given above, we can argue that counterfactual effects are a manifestation of contextuality that has been overlooked in the original treatment of contextuality by Kochen and Specker [39], causing unnecessary confusion about the nature of quantum contextuality. Specifically, Kochen and Specker have placed too much emphasis on the possibility that compatible measurements may exert an influence on each other, while downplaying the possibility that contextuality originates from the well-defined relation between the outcomes of incompatible measurement contexts [40][41][42][43]. Counterfactual effects illustrate this relation between incompatible measurements by introducing a minimal change of context represented by the exclusion of a single possibility.…”