Noncontextual versus contextual interferometry

TL;DR

The paper investigates which aspects of single-particle interference can be captured by classical models and which require quantum contextuality. It develops a minimal extension of Quantum Simulation Logic (QSL) to reproduce the Elitzur–Vaidman bomb tester and its improved version, clarifying how phase kickback mechanisms enable classical simulations of certain interference phenomena. By contrast, it demonstrates that Hofmann's three-path interferometer exhibits Kochen–Specker contextuality, as shown by a KCBS inequality violation, indicating that some interference phenomenology cannot be captured by noncontextual classical models. The work thereby sharpens the boundary between classical simulability and quantum contextuality, promotes Kochen–Specker contextuality as a resource indicator for quantum advantage, and situates these findings within broader discussions of Boson sampling and quantum technologies. Overall, it provides a clearer, simpler alternative to prior approaches and delineates where contextuality is essential for capturing quantum interference.

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.

Figures (6)

• Figure 1: The Elitzur-Vaidman Bomb Tester. (a) Bomb doesn't work so it does not interact with the photon. (b) Bomb works, so detects photons that arrive at the bomb. We show in Section \ref{['sect.EV']} that we can reproduce the peculiar behaviour of this scenario classically, using a minimal extension of QSL.
• Figure 2: Zero- or one-photon beam-splitter in second quantization (left), Quantum Simulation Logic circuit that reproduces noncontextual behaviour mimicking this beamsplitter (right).
• Figure 3: The Elitzur-Vaidman improved bomb tester that uses unbalanced beamsplitters. (a) Bomb doesn't work so it does not interact with the photon. (b) Bomb works, so detects photons that arrive at the bomb. We show in Section \ref{['sect.EVImproved']} that we can reproduce the peculiar behaviour of this scenario classically, using a small extension of QSL.
• Figure 4: Detection probabilities in a three-path interferometer with indicated beamsplitter ratios. Input state $\frac{1}{\sqrt3}(\left| 100 \right\rangle+\left| 010 \right\rangle+\left| 001 \right\rangle)$.
• Figure 5: The five different contexts for KCBS violation. The input state is $\frac{1}{\sqrt3}(\left| 100 \right\rangle+\left| 010 \right\rangle+\left| 001 \right\rangle)$. For details on how to compare $A_1$ and $A_1'$ see text.