2008/02/01 by Berthold‐Georg Englert, BERTHOLD-GEORG ENGLERT, DAGOMIR KASZLIKOWSKI +5 · 3 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Astronomical interferometer #Computer science #Duality (order theory) #Generalization #Interference (communication) #Interferometry #Mathematical analysis #Mathematics #Mechanical and Optical Resonators #Optics #Path (computing) #Photonic and Optical Devices #Physics #Pure mathematics #Quantum #Quantum Information and Cryptography #Quantum mechanics #Telecommunications #Theoretical physics #Visibility #Wave–particle duality
paper · doi:10.1142/s0219749908003220
crossref issued 2008/02/01 · crossref published 2008/02/01 · crossref published-print 2008/02/01 · openalex publication_date 2008/02/01 · crossref created 2008/02/04 · crossref published-online 2011/11/21 · crossref deposited 2021/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/11 · crossref indexed 2026/08/06
For two-path interferometers, the which-path predictability [Formula: see text] and the fringe visibility [Formula: see text] are familiar quantities that are much used to talk about wave-particle duality in a quantitative way. We discuss several candidates that suggest themselves as generalizations P of [Formula: see text] for multi-path interferometers, and treat the case of three paths in considerable detail. To each choice for the path knowledge P, the interference strength V — the corresponding generalization of [Formula: see text] — is found by a natural, operational procedure. In experimental terms, it amounts to finding those equal-weight superpositions of the path amplitudes which maximize P for the emerging intensities. Mathematically speaking, one needs to identify a certain optimum one among the Fourier transforms of the state of the interfering quantum object. Wave-particle duality is manifest, inasmuch as P = 1 implies V = 0 and V = 1 implies P = 0, whatever definition is chosen. The possible values of the pair (P,V) are restricted to an area with corners at (P,V) = (0,0), (P,V) = (1,0), and (P,V) = (0,1), with the shape of the border line from (1,0) to (0,1), depending on the particular choice for P and the induced definition of V.