Chongfan Technology
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20
2025
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03
Light | The Conservation Law between Wave-Particle Duality and Entanglement
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Introduction
Wave-particle duality and entanglement are fundamental concepts in quantum physics, but their exact relationship has long remained a mystery.Professor Zhihao Ma's research group at Shanghai Jiao Tong University, in collaboration withProfessor Shaoming Fei of Capital Normal University/Max Planck Institute of Germany,、Ziwu Rui, chief scientist of Wenyao Technology,、and Yunlong Xiao, senior scientist at the Agency for Science, Technology and Research (A*STAR), Singapore,have established a theoretical framework unifying wave-particle duality and entanglement. They have provided a conservation law between wave-particle duality and entanglement, revealing the deep connection between the two.Professor Jianwei Wang's team at Peking Universityhas experimentally verified this through silicon-integrated nano-photonic quantum chips.
Recently, the relevant research results were published inLight: Science & Applicationsunder the title "Light: Science & Applications。
Research Background
Light is both a wave and a particle; this is wave-particle duality, one of the most puzzling aspects of quantum mechanics. Wave-particle duality is the foundation of quantum mechanics; Nobel laureate Richard Feynman called it "a true mystery of quantum mechanics." Only by understanding wave-particle duality can we truly understand quantum mechanics. Quantum entanglement, as a non-classical correlation, has also been experimentally verified.
Although wave-particle duality is a long-standing problem in quantum mechanics, Bohr proposed the complementarity principle in the early days of quantum mechanics to explain the relationship between wave-particle duality, but how to quantify the wave and particle properties of a particle has always been a difficult problem. It wasn't until 1979 that Wootters et al. first proposed a method for quantifying wave-particle duality. Then, in 1996, Englert further refined this quantification method, proposing an inequality, the famous wave-particle duality duality relationship.
In the double-slit experiment proposed by Englert, a photon may pass through the upper and lower paths, and a detector behind the path determines which path the photon has taken. At the same time, interference fringes will appear on the screen, with the wave property related to the brightest and darkest interference fringes. The particle property measures the ability to determine the particle's path; if the particle property equals 1, it means that the particle's path can be accurately determined. Later, some scholars proposed axioms for measuring wave and particle properties, and a large number of related studies emerged. These studies mainly focused on finding measures that satisfy these axioms, thereby obtaining new wave-particle duality duality relationships.
Figure 1: Schematic diagram of the double-slit interference experiment
Although methods for quantifying wave-particle duality have been found, another problem has arisen: the complementary relationship of wave-particle duality is described by an inequality. Is this inequality precise, or can it be transformed into an equation? We hope to find the missing element in the wave-particle duality relationship so that the original inequality can be transformed into an equation.
Based on this problem, Professor Zhihao Ma's research group at Shanghai Jiao Tong University, in collaboration with Professor Shaoming Fei of Capital Normal University/Max Planck Institute of Germany and Dr. Yunlong Xiao, senior scientist at A*STAR, Singapore, found that wave-particle duality and quantum entanglement have a profound internal connection. When considering the entanglement between photons and the environment, the sum of the photon's wave property measure, particle property measure, and the entanglement between the photon and the environment is always a constant. Professor Ma et al. proposed a unified theoretical framework that conveniently quantifies the magnitude of wave property, particle property, and quantum entanglement. This framework covers various common and famous wave property, particle property, and entanglement measures; it proves that there is a conservation relationship between these three measures. Specifically, for a two-photon closed system (two-body arbitrary-dimensional pure state), there is a complementary relationship between the wave and particle property measures and the quantum entanglement measure of the two-body pure state. The sum of wave property, particle property, and entanglement is always a constant, which does not depend on the choice of this two-body pure state. Professor Jianwei Wang's team at Peking University experimentally verified this conservation relationship using silicon-integrated nano-photonic quantum chips.
Figure 2: Schematic diagram of the conservation relationship between wave-particle duality and entanglement
Research Highlights
Professor Zhihao Ma's research group at Shanghai Jiao Tong University found that the wave property, particle property, and entanglement measures of a quantum state can all be uniformly obtained through the same differentiable strictly convex function. By choosing this convex function, countless legitimate measures of wave property, particle property, and entanglement can be obtained. Here, legitimate means that the measures of wave property, particle property, and entanglement all satisfy their respective reasonable axiomatic assumptions. For each convex function, it is found that the sum of the three measures of wave property, particle property, and entanglement is a constant, and this constant only depends on the dimension and the selected function. In this way, we have actually obtained countless (not one) equal relationships between wave property, particle property, and quantum entanglement, that is, there is a conservation relationship between the three, which is not a mathematical coincidence, but indicates that these three key physical quantities do indeed have a profound internal connection, and therefore a unified conservation law can be obtained.
Professor Jianwei Wang's team at Peking University verified this theory using silicon-integrated nano-photonic quantum chips. The experiment not only verified the quantum bit system (two-dimensional case), but also verified the two-dimensional, three-dimensional, and four-dimensional quantum states. Regardless of the dimension of the quantum state, the experimental results are highly consistent with the theory, again showing that the conservation relationship between wave-particle duality and entanglement is universal. This is also the first experimental verification of the wave-particle duality dual relationship for high-dimensional quantum states; previous experiments were based on quantum bit systems. On the other hand, for the case of two-body mixed states (i.e., two-body open systems), the conservation relationship is found not to hold theoretically, but becomes an inequality relationship, and the experimental results also verify this theoretical prediction. From an information theory perspective, this indicates that in an open system, some information is dissipated into the environment, resulting in a reduction in the total amount of information, and thus the conservation relationship no longer holds.
Figure 3.a Experimental circuit diagram; b Experimental setup diagram
Summary and Outlook
This research proposes a unified theoretical framework that can uniformly quantify wave property, particle property, and quantum entanglement, finding that the conservation relationship between the three is universal. At the same time, the conservation relationship was experimentally verified for high-dimensional quantum systems using silicon-integrated nano-photonic quantum chips. This research not only deepens our understanding of the relationship between wave-particle duality and entanglement, but also promotes in-depth research on fundamental problems in quantum mechanics and discovers new technological applications in fields such as quantum precision measurement.
Paper Information
Ding Z., Deng Y., Fei SM. et al. Universal conservation law for wave-particle-entanglement triplets: theory and experiment. Light Science & Applications 14, 82 (2025).
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