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Advanced Photonics

Wave-particle duality in orbital angular momentum-based quantum delayed-choice experiment

Da-Wei Lyu, Qian-ke Wang, Jun Liu, Jian Wang

Published Jun 18, 2026• 0 citations
Publisher

Abstract

Wave-particle duality is a foundational feature of quantum mechanics and can be demonstrated via delayed-choice and quantum delayed-choice (QDC) experiments. Photon-based implementations commonly rely on polarization or path degrees of freedom (DoFs), but these approaches present limitations: polarization is restricted to two dimensions, and the path-based schemes, although scalable, face increasing challenges in optical complexity and interferometric stability as the dimensionality grows. Here, we present a scalable QDC scheme leveraging the orbital angular momentum (OAM) of photons that overcomes these limitations. Instead of directly encoding paths in OAM states, we encode qubits in subsystems of the OAM DoF—specifically its signs and amplitudes—and realize a controlled-Hadamard gate with 98.73(2)% fidelity on these qubits using a diffractive neural network. This allows us to demonstrate the QDC experiment within the OAM subsystems and observe interference transitions between wave-like and particle-like behaviors in the space structured by these subsystems, with fidelities exceeding 99%. Our results show that wave-particle duality extends beyond intrinsic DoFs to qubits encoded in internal substructures of those DoFs, offering a broader perspective on the fundamental nature of quantum behavior.

DOI
10.1117/1.ap.8.4.046004

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Wave-particle duality is a foundational feature of quantum mechanics and can be demonstrated via delayed-choice and quantum delayed-choice (QDC) experiments. Photon-based implementations commonly rely on polarization or path degrees of freedom (DoFs), but these approaches present limitations: polarization is restricted to two dimensions, and the path-based schemes, although scalable, face increasing challenges in optical complexity and interferometric stability as the dimensionality grows. Here, we present a scalable QDC scheme leveraging the orbital angular momentum (OAM) of photons that overcomes these limitations. Instead of directly encoding paths in OAM states, we encode qubits in subsystems of the OAM DoF—specifically its signs and amplitudes—and realize a controlled-Hadamard gate with 98.73(2)% fidelity on these qubits using a diffractive neural network. This allows us to demonstrate the QDC experiment within the OAM subsystems and observe interference transitions between wave-like and particle-like behaviors in the space structured by these subsystems, with fidelities exceeding 99%. Our results show that wave-particle duality extends beyond intrinsic DoFs to qubits encoded in internal substructures of those DoFs, offering a broader perspective on the fundamental nature of quantum behavior.
Abstract Wave-particle duality is a foundational yet counterintuitive feature of quantum mechanics, typically demonstrated via delayed-choice and quantum delayed-choice (QDC) experi ments. Photon-based implementations commonly rely on polarization or path degrees of freedom (DoFs), but these approaches present limitations: polarization is restricted to two dimensions, and the path-based schemes, while scalable, face increasing challenges in opti cal complexity and interferometric stability as the dimensionality grows. Here, we present a scalable QDC scheme leveraging the orbital angular momentum (OAM) of photons that overcomes these limitations. Instead of directly encoding paths in OAM states, we encode qubits in subsystems of the OAM DoF—specifically, its signs and amplitudes—and real ize a controlled-Hadamard (CH) gate with 98.73±0.02% fidelity on these qubits using a diffractive neural network. This allows us to demonstrate the QDC experiment within the OAM subsystems, achieving interference transitions between wave-like and particle like behaviors, with fidelities exceeding 99%. Our results show that wave-particle duality extends beyond intrinsic DoFs to qubits encoded in internal substructures of those DoFs, offering a broader perspective on the fundamental nature of quantum behavior.
Bohr’s complementarity is one central tenet of quantum physics. The paradoxical wave-particle duality of quantum matters and photons has been tested in Young’s double-slit (double-path) interferometers. The object exclusively exhibits wave and particle nature, depending measurement apparatus that can be delayed chosen to rule out too-naive interpretations of quantum complementarity. All experiments to date have been implemented in the double-path framework, while it is of fundamental interests to study complementarity in multipath interferometric systems. Here we demonstrate generalised multipath wave-particle duality in a quantum delayed-choice experiment, implemented by large-scale silicon-integrated multipath interferometers. Single-photon displays sophisticated transitions between wave and particle characters, determined by the choice of quantum-controlled generalised Hadamard operations. We characterise particle-nature by multimode which-path information and wave-nature by multipath coherence of interference, and demonstrate the generalisation of Bohr’s multipath duality relation. Our work provides deep insights into multidimensional quantum physics and benchmarks controllability of integrated photonic quantum technology.
Wheeler's delayed-choice experiment delays the decision to observe either the wave or particle behavior of a photon until after it has entered the interferometer, and the quantum delayed-choice experiment provides the possibility of observing the wave and particle behaviors with a single experimental setup by introducing quantum control. We here propose a modified quantum delayed-choice experiment without quantum control or entanglement assistance, in which a photon can be prepared in a wave-particle superposition state and the morphing behavior of wave-to-particle transition can be observed easily. It is demonstrated that the presented scheme can allow us to rule out classical hidden-variable models in a device-independent manner via violating dimension witness. We also extend the scheme to the situation of two degrees of freedom, first constructing a hybrid quantum delayed-choice experiment which enables a photon respectively exhibits wave and particle behaviors in different degrees of freedom, and then proposing a scheme to prepare the single-photon wave-particle entanglement. This study is not only meaningful to explore the wave-particle complementarity of photons, but also provides potential for the research of the single-particle nonlocality from the perspective of the wave-particle degree of freedom.
Abstract Bohr’s complementarity is one central tenet of quantum physics. The paradoxical wave-particle duality of quantum matters and photons has been tested in Young’s double-slit (double-path) interferometers. The object exclusively exhibits wave and particle nature, depending measurement apparatus that can be delayed chosen to rule out too-naive interpretations of quantum complementarity. All experiments to date have been implemented in the double-path framework, while it is of fundamental interest to study complementarity in multipath interferometric systems. Here, we demonstrate generalized multipath wave-particle duality in a quantum delayed-choice experiment, implemented by large-scale silicon-integrated multipath interferometers. Single-photon displays sophisticated transitions between wave and particle characters, determined by the choice of quantum-controlled generalized Hadamard operations. We characterise particle-nature by multimode which-path information and wave-nature by multipath coherence of interference, and demonstrate the generalisation of Bohr’s multipath duality relation. Our work provides deep insights into multidimensional quantum physics and benchmarks controllability of integrated photonic quantum technology.
Bohr's complementarity is one central tenet of quantum physics. The paradoxical wave-particle duality of quantum matters and photons has been tested in Young's double-slit (double-path) interferometers. The object exclusively exhibits wave and particle nature, depending measurement apparatus that can be delayed chosen to rule out too-naive interpretations of quantum complementarity. All experiments to date have been implemented in the double-path framework, while it is of fundamental interest to study complementarity in multipath interferometric systems. Here, we demonstrate generalized multipath wave-particle duality in a quantum delayed-choice experiment, implemented by large-scale silicon-integrated multipath interferometers. Single-photon displays sophisticated transitions between wave and particle characters, determined by the choice of quantum-controlled generalized Hadamard operations. We characterise particle-nature by multimode which-path information and wave-nature by multipath coherence of interference, and demonstrate the generalisation of Bohr's multipath duality relation. Our work provides deep insights into multidimensional quantum physics and benchmarks controllability of integrated photonic quantum technology.
In this work, we revisit the previously demonstrated experiment called the quantum delayed-choice experiment [Phys. Rev. Lett.107, 230406 (2011)PRLTAO0031-900710.1103/PhysRevLett.107.230406], which shows that it is possible to reveal the wave and particle nature of photons simultaneously. After discussing the main points of this paper concerning the fundamental aspect of wave-particle duality, we demonstrate theoretically that the same observation can be achieved by operating on the polarization state of a photon. For this purpose, we apply the same operators, except that they transform the polarization states, whereas mode operation was performed in the previous work.