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Light Science & Applications

Universal conservation laws of the wave-particle-entanglement triad: theory and experiment

Ziheng Ding, Yaohao Deng, Shao-Ming Fei, Si-Qi Zhou, Xiaojiong Chen, Ziwen Rui, Zhihao Ma, Yunlong Xiao, Jianwei Wang

Published Feb 11, 2025• 13 citations
Publisher

Abstract

When observed, a quantum system exhibits either wave-like or particle-like properties, depending on how it is measured. However, this duality is affected by the entanglement of the system with its quantum memory, raising a fundamental question: how are wave-particle duality and entanglement related? Here, we broaden the scope of wave-particle duality to include entanglement, introduce universal conservation laws for the wave-particle-entanglement triad, and perform demonstrations on silicon-integrated nanophotonic quantum chips. Our experiments not only mark the first confirmation of universal conservation laws but also highlight the potential of integrated photonics for exploring complex quantum phenomena in high-dimensional systems.

DOI
10.1038/s41377-025-01759-4

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When observed, a quantum system exhibits either wave-like or particle-like properties, depending on how it is measured. However, this duality is affected by the entanglement of the system with its quantum memory, raising a fundamental question: how are wave-particle duality and entanglement related? Here, we broaden the scope of wave-particle duality to include entanglement, introduce universal conservation laws for the wave-particle-entanglement triad, and perform demonstrations on silicon-integrated nanophotonic quantum chips. Our experiments not only mark the first confirmation of universal conservation laws but also highlight the potential of integrated photonics for exploring complex quantum phenomena in high-dimensional systems.
The wave-particle duality of quantum objects has been a center concept in quantum mechanics since its birth. For the two-path or two-slit experiment, the dual nature of quantum matter has been well studied in various systems. To rule out the interpretation of quanta knowing the measurement setting it will be confronted, Wheeler proposed the famous delayed-choice gedanken experiment [1] , which is an ideal platform to test the intrinsic characters of wave-particle duality. However, all these experiments to date have been focused on the two-path case.
Stunning progress in the experimental resolution and control of natural or man-made complex systems at the level of their quantum mechanical constituents raises the question, across diverse subdisciplines of physics, chemistry, and biology, whether the fundamental quantum nature may condition the dynamical and functional system properties on mesoscopic if not macroscopic scales. However, which are the distinctive signatures of quantum properties in complex systems, notably when modulated by environmental stochasticity and dynamical instabilities? It appears that, to settle this question across the above communities, a shared understanding is needed of the central feature of quantum mechanics: wave-particle duality. In this Perspective, we elaborate how randomness induced by this very quantum property can be discerned from the stochasticity ubiquitous in complex systems already on the classical level. We argue that in the study of increasingly complex systems, such distinction requires the analysis of single incidents of quantum dynamical processes.
One of the cornerstones of quantum physics is the wave nature of matter. It explains experimentally observed effects like interference and diffraction, occurring when an object moves from one place to another along several indistinguishable ways simultaneously. The wave nature disappears when the individual ways are distinguishable. In this case, the particle nature of the object becomes visible. To determine the particle nature quantitatively, the way of the object has to be measured. Here, large progress has been made recently with new techniques, enabling one to investigate single moving atoms in a controlled manner. Two examples are discussed in the following two sections. The first experiment describes an atom interferometer, where the way of the atom is entangled with its internal state. This allows one to explore the origin of wave-particle duality and perform a quantitative test of this fundamental principle. The second experiment reports on the observation of an atom-photon molecule, a bound state between an atom and a single photon. A fascinating aspect of this system is that it makes possible to monitor the motion of a single neutral atom in real time.
Quantum theory reveals astonishing and counterintuitive phenomena not found in classical physics, such as wave-particle duality, where entities like electrons and photons exhibit both wave-like and particle-like behaviors. In this paper, we leverage advancements in quantum information science to gain new insights into this phenomenon. We specifically examine negative conditional entropy in quantum entanglement, where the selection of the measurement basis appears to ripple backward in time, akin to Dirac's model of an infinite sea of negative energy states filled with electrons, where holes in this sea appear as positrons. We propose that an observer's knowledge of the measurement choice, analogous to a hole in the negative information sea, corresponds to the wave aspect of the system, while the classical outcome aligns with its particle nature. This exploration of the relationship between microscopic quantum phenomena and macroscopic observations offers new perspectives on the mind-matter duality.
Abstract Single-photon entanglement, the entanglement between vacuum state and single-photon state, is essentially the entanglement of particle characteristics. Wave-particle duality indicates that wave property and particle property could coexist. Can we find evidence of wave-behavior entanglement in single-photon entanglement? Here, based on the construction of Bell-like inequality in wave space, we propose a method to verify the wave-particle duality in single-photon entanglement. First, we define the wave state in two-dimensional space relative to the photon number state, and propose a method to measure the wave state. The strong violation of Bell’s inequality based on the joint measurement of wave states indicates the existence of single-photon entanglement, and the wave is the conjugate variable of the particle. Wave state entanglement obtained from Fourier transform of single photon entanglement and the corresponding measurement protocols will provide us with more information-carrying schemes in the field of quantum information. The difference in the representation in photon-number space and wave space implies the wave-particle duality of single photon entanglement.
Abstract One of the cornerstones of quantum physics is the wave nature of matter. It explains experimentally observed effects like interference and diffraction, occurring when an object moves from one place to another along several indistinguishable ways simultaneously. The wave nature disappears when the individual ways are distinguishable. In this case, the particle nature of the object becomes visible. To determine the particle nature quantitatively, the way of the object has to be measured. Here, large progress has been made recently with new techniques, enabling one to investigate single moving atoms in a controlled manner. Two examples are discussed in the following two sections. The first experiment describes an atom interferometer, where the way of the atom is entangled with its internal state. This allows one to explore the origin of wave‐particle duality and perform a quantitative test of this fundamental principle. The second experiment reports on the observation of an atom‐photon molecule, a bound state between an atom and a single photon. A fascinating aspect of this system is that it makes possible to monitor the motion of a single neutral atom in real time.