Wave-particle duality is one of the most notable and counterintuitive features of quantum mechanics, illustrating that two incompatible observables cannot be measured simultaneously with arbitrary precision. In this work, we experimentally demonstrate the equivalence of wave-particle duality and entropic uncertainty relations using orbital angular momentum (OAM) states of light. Our experiment uses an innovative and reconfigurable platform composed of few-mode optical fibers and photonic lanterns, showcasing the versatility of this technology for quantum information processing. Our results provide fundamental insights into the complementarity principle from an informational perspective, with implications for the broader field of quantum technologies.
Wave-particle duality is one of the most notable and counterintuitive features of quantum mechanics, illustrating that two incompatible observables cannot be measured simultaneously with arbitrary precision. In this work, we experimentally demonstrate the equivalence of wave-particle duality and entropic uncertainty relations using orbital angular momentum (OAM) states of light. Our experiment uses an innovative and reconfigurable platform composed of few-mode optical fibers and photonic lanterns, showcasing the versatility of this technology for quantum information processing. Our results provide fundamental insights into the complementarity principle from an informational perspective, with implications for the broader field of quantum technologies.
Abstract Wave-particle duality (WPD) is known to be equivalent to an entropic uncertainty relation (EUR) based on the min- and max-entropies, which have a clear operational meaning in quantum cryptography. Here, we derive a connection between wave-particle relations and the semi-device-independent (SDI) security framework. In particular, we express an SDI witness entirely in terms of two complementary interferometric quantities: visibility and input distinguishability. Applying a symmetry condition to the interferometric quantities, we identify a scenario in which the classical bound is violated and the security condition is met in wave-particle experiments with a tunable beam splitter (TBS). This enables the certification of non-classicality and the positivity of the key rate directly from complementary interferometric quantities, as well as from informational entropic quantities. Moreover, we perform a proof-of-principle experiment using orbital-angular-momentum (OAM) encoded quantum states of light in a tunable interferometer, validating our theoretical predictions. We analyze an improved bound on the SDI security condition for qubits, effectively enlarging the parameter region where secure communication can be certified. Finally, we extend the framework to multipath interferometers, establishing that the fundamental correspondence between information-access limitations and interferometric complementarity, demonstrated in the two-path scenario, persists across arbitrary dimensions.
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 The wave-particle duality, as a manifestation of Bohr’s complementarity, is usually quantified in terms of path predictability and interference visibility. Various characterizations of the wave-particle duality have been proposed from an operational perspective, most of them are in forms of inequalities, and some of them are expressed in forms of equalities by incorporating entanglement or coherence. In this work, we shed different insights into the nature of the wave-particle duality by casting it into a form of information conservation in a multi-path interferometer, with uncertainty as a unified theme. More specifically, by employing the simple yet fundamental concept of variance, we establish a resolution of unity, which can be interpreted as a complementarity relation among wave feature, particle feature, and mixedness of a quantum state. This refines or reinterprets some conventional approaches to wave-particle duality, and highlights informational aspects of the issue. The key idea of our approach lies in that a quantum state, as a Hermitian operator, can also be naturally regarded as an observable, with measurement uncertainty (in a state) and state uncertainty (in a measurement) being exploited to quantify particle feature and wave feature of a quantum state, respectively. These two kinds of uncertainties, although both are defined via variance, have fundamentally different properties and capture different features of a state. Together with the mixedness, which is a kind of uncertainty intrinsic to a quantum state, they add up to unity, and thus lead to a characterization of the wave-particle-mixedness complementarity. This triality relation is further illustrated by examples and compared with some popular wave-particle duality or triality relations.
One of the most remarkable features of quantum physics is that attributes of quantum objects, such as the wavelike and particlelike behaviors of single photons, can be complementary in the sense that they are equally real but cannot be observed simultaneously. Quantum measurements, serving as windows providing views into the abstract edifice of quantum theory, are basic tools for manifesting the intrinsic behaviors of quantum objects. However, a quantitative formulation of complementarity that highlights its manifestations in general measurement scenarios remains elusive. Here we develop a general framework for demonstrating quantum complementarity in the form of information exclusion relations (IERs), which incorporates the wave-particle duality relations as particular examples. Moreover, we explore the applications of our theory in entanglement detection and elucidate that our IERs lead to an extended form of entropic uncertainty relations, providing insights into the connection between quantum complementarity and the preparation uncertainty.
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.