2015/12/31 by Patrick J. Coles · 67 citations
Computer Science · Mathematics · Physics and Astronomy · #Astronomical interferometer #Classical mechanics #Computer science #Duality (order theory) #Interferometry #Mathematics #Mechanical and Optical Resonators #Observable #Optics #Path (computing) #Physics #Pure mathematics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Theoretical physics #Uncertainty principle #Unification #Visibility #Wave–particle duality #quant-ph
paper · pdf · doi:10.1103/physreva.93.062111
published in Physical Review A 93(6) (American Physical Society) · 6 + 7 pages, 1 figure
arxiv created 2016/06/09 · openalex publication_date 2016/06/09 · arxiv updated 2016/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
An interferometer---no matter how clever the design---cannot reveal both the wave and the particle behavior of a quantum system. This fundamental idea has been captured by inequalities, so-called wave-particle duality relations (WPDRs), that upper bound the sum of the fringe visibility (wave behavior) and path distinguishability (particle behavior). Another fundamental idea is Heisenberg's uncertainty principle, stating that some pairs of observables cannot be known simultaneously. Recent work has unified these two principles for two-path interferometers. Here we extend this unification to n-path interferometers, showing that WPDRs correspond to a modern formulation of the uncertainty principle stated in terms of entropies. Furthermore, our unification provides a framework for solving an outstanding problem of how to formulate universally valid WPDRs for interferometers with more than two paths, and we employ this framework to derive some novel WPDRs.