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Quantum Communications and Quantum Imaging

Contextuality and inequality violations in a three-path interferometer

Ming Ji, M. Iinuma, Holger Friedrich Hofmann

Published Oct 3, 2023• 1 citation
Publisher

Abstract

Quantum contextuality can be observed in three path interferometers, suggesting a fundamental contradiction between wave propagation and particle propagation inherent in the wave-particle dualism. Here, we investigate this contradiction in a three path interferometer specifically designed to illustrate the paradoxical aspects of single particle interference. A particularly clear violation of non-contextual assumptions is obtained when interference effects suppress detection probabilities to zero in paths that seem to be necessary to explain the observation of photons in the output. This contradiction between detection probabilities in the paths and detection probabilities in the output cannot be explained by any assignment of photon paths through the interferometer, demonstrating a fundamental incompatibility of wave propagation and particle propagation.

DOI
10.1117/12.2674958

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Quantum contextuality can be observed in three path interferometers, suggesting a fundamental contradiction between wave propagation and particle propagation inherent in the wave-particle dualism. Here, we investigate this contradiction in a three path interferometer specifically designed to illustrate the paradoxical aspects of single particle interference. A particularly clear violation of non-contextual assumptions is obtained when interference effects suppress detection probabilities to zero in paths that seem to be necessary to explain the observation of photons in the output. This contradiction between detection probabilities in the paths and detection probabilities in the output cannot be explained by any assignment of photon paths through the interferometer, demonstrating a fundamental incompatibility of wave propagation and particle propagation.
Quantum contextuality describes scenarios in which it is impossible to explain the experimental evidence in terms of a measurement-independent reality. Here a three-path interferometer is introduced in which all five contexts needed for a demonstration of contextuality are realized in sequence. It is then possible to observe a paradoxical situation where the paths connecting input ports to their corresponding output ports appear to be blocked by destructive interference. It is shown that the conditional currents observed in weak measurements provide a consistent explanation of the paradox, indicating that weak values might help to bridge the gap between wave-like propagation effects and local particle detection.
Quantum information is based on the apparent contradictions between classical logic and quantum coherence described by Kochen-Specker contextuality. Surprisingly, this contradiction can be demonstrated in a comparatively simple three-path interferometer, where it is impossible to trace the path of a single photon through five consecutive stages of the interferometer. Here, I discuss the paradoxical aspects of single photon interferences revealed by the three-path interferometer and point out the essential role of dynamics in quantum information.
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.
As shown in previous work, quantum contextuality can be represented by interference effects in a three-path interferometer. A Hardy-like paradox is obtained when the absence of photons in two internal paths seems to contradict the presence of photons in a specific input port. Here, we consider the effects of counterfactual control on this scenario by analyzing the changes to the paths through the interferometer when the seemingly impossible input path is blocked. The effects on photons that never interact with the absorber in the blocked path reveals a characteristic signature of quantum contextuality that may help to explain why quantum interference is incompatible with measurement independent realities.
Quantum contextuality, where measurement outcomes depend on the measurement context, implies a failure of classical realism in quantum systems. As recently shown, the transition between measurement contexts can be mapped onto the path that a quantum particle takes through an interferometer. Here, we investigate the relation between contextuality and the counterfactual gain observed in the output ports of such an interferometer when one of the paths is blocked. It is shown that experimental evidence of contextuality can only be obtained when counterfactual gain is observed for a specific combination of blocked path and output port. Using a silicon photonic integrated circuit, we experimentally observe the counterfactual gain for a selection of input states and evaluate the associated evidence for contextuality. The results confirm that contextuality can only be observed in the presence of counterfactual gain.
Abstract Basic quantum effects are often illustrated using single particle interferences in two-path interferometers. A wider range of non-classical phenomena can be illustrated using three-path interferometers, but the increased complexity of quantum statistics in a three-dimensional Hilbert space makes it difficult to identify a representative set of observable properties that could be used to characterize specific phenomena. Here, I propose a characterization of pure states based on a five-stage interferometer recently introduced to demonstrate the relation between different measurement contexts (Optica Quantum 1, 63 (2023)). It is shown that the orthogonality relations between the states representing the different measurement contexts can be used to classify pure states within the three-dimensional Hilbert space according to the non-classical correlations between different contexts expressed by negative Kirkwood–Dirac distributions.