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arXiv:1407.2930 · Reviews of Modern Physics

Delayed-choice gedanken experiments and their realizations

Xiao‐Song Ma, Johannes Kofler, Anton Zeilinger

Published Mar 3, 2016• 222 citations
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Abstract

Wave-particle duality lies at the root of quantum mechanics and is central in the description of interferences observed with elementary objects. In a delayed-choice experiment, the decision to observe the particle or wave character of a quantum system is delayed with respect to the time at which the system enters the interferometer. This paper reviews the history of the delayed-choice idea, introduced as a challenge to a realistic explanation of the wave-particle duality. It also describes recent experimental realizations of this idea and discusses intriguing extensions, such as the duality between separability and entanglement in multiple quantum systems.

DOI
10.1103/revmodphys.88.015005

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Wave-particle duality lies at the root of quantum mechanics and is central in the description of interferences observed with elementary objects. In a delayed-choice experiment, the decision to observe the particle or wave character of a quantum system is delayed with respect to the time at which the system enters the interferometer. This paper reviews the history of the delayed-choice idea, introduced as a challenge to a realistic explanation of the wave-particle duality. It also describes recent experimental realizations of this idea and discusses intriguing extensions, such as the duality between separability and entanglement in multiple quantum systems.
Delaying Quantum Choice Photons can display wavelike or particle-like behavior, depending on the experimental technique used to measure them. Understanding this duality lies at the heart of quantum mechanics. In two reports, Peruzzo et al. (p. 634 ) and Kaiser et al. (p. 637 ; see the Perspective on both papers by Lloyd ) perform an entangled version of John Wheeler's delayed-choice gedanken experiment, in which the choice of detection can be changed after a photon passes through a double-slit to avoid the measurement process affecting the state of the photon. The original proposal allowed the wave and particle nature of light to be interchanged after the light had entered the interferometer. By contrast in this study, entanglement allowed the wave and particle nature to be interchanged after the light was detected and revealed the quantum nature of the photon, for example, it displays wave- and particle-like behavior simultaneously.
Wave-particle duality constitutes one of the most intriguing features in quantum physics. A well-known gedanken experiment that provides evidence for this is Wheeler's delayed-choice experiment based on a Mach-Zehnder interferometer [J. A. Wheeler, in Mathematical Foundations of Quantum Theory, edited by A. R. Marlow (Academic, New York, 1978), pp. 9--48; in Quantum Theory and Measurement, edited by J. A. Wheeler and W. H. Zurek (Princeton University Press, Princeton, 1984), pp. 182--213]. Many different versions of delayed-choice experiments have been conducted with both classical and quantum detecting devices. Recently, it was proposed that the delayed-choice experiment could be devised from the perspective of a device-independent prepare-and-measure scenario [R. Chaves et al., Causal Modeling the Delayed-Choice Experiment, Phys. Rev. Lett. 120, 190401 (2018)]. In our work, we experimentally realize this modified version with a deterministic single-photon source and examine the wave-particle objective in a causal-modeled scheme without the assistance of entanglement, which is achieved by violating the dimension-witness inequalities. Our experiment also provides an intriguing perspective and exhibits the benefits of studying quantum theory from the casual model point of view.
Wheeler’s gedanken experiment is the most fascinating and subtle illustration of wave-particle duality [1]. If we consider a single-photon light pulse in a Mach-Zehnder interferometer, one can either measure the interference at the output – evidencing the “wave-like” behavior of the photon- or one can detect the path followed by the photon – evidencing its “particle-like” behavior. In order to pinpoint how surprising this is, John Wheeler considered a “delayed-choice” regime where the choice of measuring either property is done only after the photon has entered the interferometer.
Wave-particle duality is strikingly illustrated by Wheeler's delayed-choice gedanken experiment, where the configuration of a two-path interferometer is chosen after a single-photon pulse has entered it: Either the interferometer is closed (that is, the two paths are recombined) and the interference is observed, or the interferometer remains open and the path followed by the photon is measured. We report an almost ideal realization of that gedanken experiment with single photons allowing unambiguous which-way measurements. The choice between open and closed configurations, made by a quantum random number generator, is relativistically separated from the entry of the photon into the interferometer.
The wave–particle duality is the quintessence of quantum mechanics. This duality gives rise to distinct behaviors depending on the experimental setup, with the system exhibiting either wave-like or particle-like properties, depending on whether the focus is on interference (wave) or trajectory (particle). In the interaction with a beam splitter, photons with particle behavior can transform into a wave behavior and vice versa. In Wheeler’s delayed-choice gedanken experiment, this interaction is delayed so that the wave that initially travels through the interferometer can become a particle, avoiding the interaction. We show that this contradiction can be resolved using polarized entangled photon pairs. An analysis of Shannon’s entropy supports this proposal.
The delayed-choice experiment has long been regarded as one of the most conceptually intriguing demonstrations in quantum mechanics because the measurement configuration can be selected after a quantum system has already entered the experimental apparatus. This feature has often been interpreted as suggesting that the present measurement determines whether the quantum system behaved as a wave or as a particle in the past, thereby motivating discussions of wave–particle duality and retrocausality. This paper reexamines the delayed-choice experiment from the perspective of the Intrinsic Observability Framework (IOF). Rather than interpreting the experiment as demonstrating that the past is modified or that a quantum system intrinsically possesses either wave-like or particle-like properties prior to measurement, the IOF distinguishes between the pre-measurement domain of Potential Observability (PO) and the operational establishment of Observability through measurement. Within this framework, wave-like and particle-like behaviors are interpreted as observable representations established under different accessibility bases rather than intrinsic properties of the quantum system itself. Measurement grants accessibility, thereby establishing an observable representation according to the selected accessibility basis, within which observable values become operationally defined. Consequently, the delayed choice is understood not as selecting whether the quantum system was previously a wave or a particle, but as selecting the accessibility basis through which observability is established. From this perspective, the traditional wave–particle duality is reinterpreted as the basis dependence of observable representation rather than the coexistence of two fundamentally different physical natures. The delayed-choice experiment therefore illustrates how different accessibility bases lead to different observable representations while remaining fully compatible with the standard mathematical formalism of quantum mechanics.