PIRSA:14110114

Equivalence of wave-particle duality to entropic uncertaintyEquivalence of wave-particle duality to entropic uncertainty

Coles, P. (2014). Equivalence of wave-particle duality to entropic uncertaintyEquivalence of wave-particle duality to entropic uncertainty. Perimeter Institute. https://pirsa.org/14110114

Coles, Patrick. Equivalence of wave-particle duality to entropic uncertaintyEquivalence of wave-particle duality to entropic uncertainty. Perimeter Institute, Nov. 04, 2014, https://pirsa.org/14110114 

          @misc{ pirsa_PIRSA:14110114,
            doi = {10.48660/14110114},
            url = {https://pirsa.org/14110114},
            author = {Coles, Patrick},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Equivalence of wave-particle duality to entropic uncertaintyEquivalence of wave-particle duality to entropic uncertainty},
            publisher = {Perimeter Institute},
            year = {2014},
            month = {nov},
            note = {PIRSA:14110114 see, \url{https://pirsa.org}}
          }

Patrick Coles Carnegie Mellon University

DOI 10.48660/14110114
Collection
Talk Type Scientific Series
Subject

Abstract

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).