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arXiv:2308.02086 · Optica Quantum

Sequential propagation of a single photon through five measurement contexts in a three-path interferometer

Holger Friedrich Hofmann

Published Dec 1, 2023• 6 citations
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Abstract

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.

DOI
10.1364/opticaq.502468

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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 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.
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.
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.
Abstract In this paper, we investigate the possibility of explaining nonclassical correlations between two quantum systems in terms of quantum interferences between collective states of the two systems. We achieve this by mapping the relations between different measurement contexts in the product Hilbert space of a pair of two-level systems onto an analogous sequence of interferences between paths in a single-particle interferometer. The relations between different measurement outcomes are then traced to the distribution of probability currents in the interferometer, where paradoxical relations between the outcomes are identified with currents connecting two states that are orthogonal and should therefore exclude each other. We show that the relation between probability currents and correlations can be represented by continuous conditional (quasi)probability currents through the interferometer, given by weak values; the violation of the noncontextual assumption is expressed by negative conditional currents in some of the paths. Since negative conditional currents correspond to the assignment of negative conditional probabilities to measurements results in different measurement contexts, the necessity of such negative probability currents represents a failure of noncontextual local realism. Our results help to explain the meaning of nonlocal correlations in quantum mechanics, and support Feynman’s claim that interference is the origin of all quantum phenomena.
Quantum mechanics describes the relation between different measurement contexts in terms of superpositions of the potential measurement outcomes. This relation between measurement contexts makes it impossible to determine context independent realities. Here, I illustrate the problem using three path interferences that implement the three box paradox and show that the representation of the final measurement outcome as a superposition of intermediate paths describes well-defined coherences between seemingly empty paths.