Noncontextual versus contextual interferometry

Abstract

Feynman famously said that single-particle interference is ``a phenomenon which is impossible to explain in any classical way, and which has in it the heart of quantum mechanics.'' In this paper we show that some of the phenomenology of interference can be reproduced in a ``classical'' way, by reproducing the Elitzur-Vaidman Bomb Tester (including their improved version) using an extension of the quantum simulation logic (QSL) formalism. Our result improves and simplifies a previous result by Catani \emph{et al}, which relies on a much more complicated extension involving a ``toy field theory.'' We also show that not all single-particle interference can be explained by such a simple extension (including that of Catani et al), by showing that Hofmann's three-path interferometer is ``nonclassical'' in a very specific sense: it violates a Kochen-Specker-noncontextual inequality. Given that both our extension of QSL and Catani et al's extension are \emph{noncontextual} -- so do not reproduce the contextual behaviour of Hofmann's three-path interferometer -- the behaviour of that interferometer is a proper example of a phenomenon that has in it the heart of quantum mechanics, according to Feynman.