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arXiv:2211.09850 · Physical Review A

Aspects of the phenomenology of interference that are genuinely nonclassical

Lorenzo Catani, Matthew Leifer, Giovanni Scala, David Schmid, Robert W. Spekkens

Published Aug 10, 2023• 45 citations
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Abstract

The authors show that a certain wave-particle duality relation is a type of uncertainty relation whose functional form is known to be able to witness the impossibility of a noncontextual model. In this way, they show that the quantum trade-off between path distinguishability and fringe visibility can witness contextuality and they discuss the requirements on an interferometric experiment necessary for achieving a noise-robust test.

DOI
10.1103/physreva.108.022207

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The authors show that a certain wave-particle duality relation is a type of uncertainty relation whose functional form is known to be able to witness the impossibility of a noncontextual model. In this way, they show that the quantum trade-off between path distinguishability and fringe visibility can witness contextuality and they discuss the requirements on an interferometric experiment necessary for achieving a noise-robust test.
We derive a generalized wave-particle duality relation for arbitrary multipath quantum interference phenomena. Beyond the conventional notion of the wave nature of a quantum system, i.e., the interference fringe visibility, we introduce a quantifier as the normalized quantum coherence, recently defined in the framework of quantum information theory. To witness the particle nature, we quantify the path distinguishability or the which-path information based on unambiguous quantum state discrimination. Then, the Bohr complementarity principle for multipath quantum interference can be stated as a duality relation between the quantum coherence and the path distinguishability. For two-path interference, the quantum coherence is identical to the interference fringe visibility, and the relation reduces to the well-known complementarity relation. The duality relation continues to hold in the case where mixedness is introduced due to possible decoherence effects.
Publisher Summary Wave-particle duality means that a quantum object can exhibit either wave or particle properties, depending on the experimental situation. The wave nature gives rise to interference phenomena, whereas knowledge about the path taken by the object testifies to its particle nature. It is impossible to observe wave and particle properties simultaneously. Atom interferometry addresses fundamental aspects of the quantum theory of measurement in real experiments. This chapter discusses the loss of interference fringes in a which-way experiment need not be due to the Heisenberg's uncertainty relation. It demonstrates how interference can be restored by erasing the which-way information. The chapter investigated a new regime, where only incomplete which-way information is available. This allowed studying the continuous transition between wave and particle pictures and to test wave-particle duality in a quantitative manner. Future experimental investigations in this field focuses on the investigation of decoherence effects to study the transition between quantum and classical physics, leading to a more detailed understanding of the processes underlying the collapse of the wave function.
Wave-particle duality in multipath interference is fraught with issues despite substantial progress in recent years. It was experimentally shown that in certain specific conditions, getting path information in a multipath experiment can actually increase the visibility of interference. As a result, it was argued that in multipath interference experiments, visibility of interference and which-path information are not always complementary observables. In the present paper, an alternative wave-particle duality relation is presented, based on a sum of visibilities of interference from individual pairs of paths. This relation is always respected, even in the kinds of specific situations mentioned above. This sum of visibilities turns out to be related to a recently introduced measure of coherence. As one of the consequences, it provides an alternative way of experimentally measuring coherence in a multipath interference experiment. As another consequence, this relation suggests a simple way of measuring path-distinguishability in multipath interference. In addition, it resolves several outstanding issues concerning wave-particle duality in multipath interference.
Wave and particle properties of a quantum object cannot be observed simultaneously. In particular, the fringe visibility in an interferometer is limited by the amount of which-way information which can be obtained. This limit is set by the recently discovered duality relation. So far, all derivations of the duality relation are independent of Heisenberg’s uncertainty relation. Here we demonstrate that it is alternatively possible to derive the duality relation in the form of an uncertainty relation for some suitably chosen observables.
Uncertainty relations express limits on the extent to which the outcomes of distinct measurements on a single state can be made jointly predictable. The existence of nontrivial uncertainty relations in quantum theory is generally considered to be a way in which it entails a departure from the classical worldview. However, this perspective is undermined by the fact that there exist operational theories which exhibit nontrivial uncertainty relations but which are consistent with the classical worldview insofar as they admit of a generalized-noncontextual ontological model. This prompts the question of what aspects of uncertainty relations, if any, cannot be realized in this way and so constitute evidence of genuine nonclassicality. We here consider uncertainty relations describing the tradeoff between the predictability of a pair of binary-outcome measurements (e.g., measurements of Pauli X and Pauli Z observables in quantum theory). We show that, for a class of theories satisfying a particular symmetry property, the functional form of this predictability tradeoff is constrained by noncontextuality to be below a linear curve. Because qubit quantum theory has the relevant symmetry property, the fact that its predictability tradeoff describes a section of a circle is a violation of this noncontextual bound, and therefore constitutes an example of how the functional form of an uncertainty relation can witness contextuality. We also deduce the implications for a selected group of operational foils to quantum theory and consider the generalization to three measurements.
The notion of wave-particle duality may be quantified by the inequality V2+K2< 1,{V}^{2}{+K}^{2}<~1,V2+K2< 1, relating interference fringe visibility V, and path knowledge K. With a single-photon interferometer in which polarization is used to label the paths, we have investigated the relation for various situations, including pure, mixed, and partially mixed input states. A quantum-eraser scheme has been realized that recovers interference fringes even when no which way information is available to erase.