Dynamical Quantum Non-locality in Phase-Space

Abstract

Non-locality is one of the hallmarks of quantum mechanics and is responsible for paradigmatic features such as entanglement and the Aharonov-Bohm effect. Non-locality comes in to “flavours": a kinematic non-locality-arising from the structure of the Hilbert space- and a dynamical non-locality arising from the quantum equations of motion-. Despite the fact that kinematic non-locality has extensively exploited as a resource for quantum equations information and its origin has been related to the uncertainty principle, it is unable to induce any change in the probability distributions, so that the "action-at-a-distance" cannot manifest. Conversely, dynamical non-locality does create explicit changes in probability, though in a "causality-preserving" manner. The origin of non-locality of quantum measurements and its relations to the fundamental postulates of quantum mechanics, such as the uncertainty principle, have been only recently elucidated. Here we trace the origin of dynamical non-locality to the superposition principle. This relation allows us to establish and identify how the uncertainty and the superpositions principles determine the non-local character of the outcome of a quantum measurement. Thus, dynamical non-locality emerges as the responsible of the breakdown of the dynamical classic realism and therefore, a key feature in the classical-quantum transition. Most importantly, being based on group theoretical and path integral formulations, our formulation admits immediate generalizations and extensions to, e.g., quantum field theory.