Scientific Series

Interferometers capture a basic mystery of quantum mechanics: a single particle can exhibit wave behavior, yet that wave behavior disappears when one tries to determine the particle's path inside the interferometer. This idea has been formulated quantitatively as an inequality, e.g., by Englert and Jaeger, Shimony, and Vaidman, which upper bounds the sum of the interference visibility and the path distinguishability. Such wave-particle duality relations (WPDRs) are often thought to be conceptually inequivalent to Heisenberg's uncertainty principle, although this has been debated. Here we show that WPDRs correspond precisely to a modern formulation of the uncertainty principle in terms of entropies, namely the min- and max-entropies. This observation unifies two fundamental concepts in quantum mechanics. Furthermore, it leads to a robust framework for deriving novel WPDRs by applying entropic uncertainty relations to interferometric models (arXiv reference: 1403.4687).

We discuss a topological description of the confining phase of (Super-)Yang-Mills theories with gauge group SU(N) which encodes all the Aharonov-Bohm phases of configurations of non-local operators. This topological action shows an additional 1-form gauge symmetry. After the introduction of domain walls, this 1-form gauge symmetry demands the appearance of new fields on the worldvolume of the wall. These new fields have a topological Chern-Simons action at level N, also suggested by string theory constructions.