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arXiv:2507.00679 · npj Quantum Information

Certifying semi-device-independent security via wave-particle duality experiments

Chithra Raj, Tushita Prasad, Anubhav Chaturvedi, Lucas da Silva Pollyceno, Daniel Spegel-Lexne, Santiago Gómez, Joakim Argillander, Alvaro Alarcón, GUILHERME BARRETO XAVIER, Marcin Pawłowski, Pedro R. Dieguez

Published Dec 23, 2025• 4 citations

Abstract

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.

DOI: 10.1038/s41534-025-01160-4

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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.

An interferometer - no matter how clever the design - cannot allow the experimenter to see both the wave and particle behavior of a quantum system. This fundamental idea has been captured quantitatively by inequalities, so-called wave-particle duality relations (WPDRs), that upper bound the sum of the path distinguishability (particle behavior) and fringe visibility (wave behavior). Another fundamental quantum concept is Heisenberg's uncertainty principle, stating that some pairs of observables cannot be known simultaneously. The distinction between these two concepts has been debated in the literature. Here we provide closure to the debate by showing that WPDRs correspond to a modern formulation of the uncertainty principle, namely, the uncertainty relation for the min- and max-entropies, which is used in quantum cryptography. At the technical level, our unification relies on a novel operational meaning for the max-entropy in terms of the guessing probability. Furthermore, our unification provides a framework for solving an outstanding problem of how to rigorously prove WPDRs for interferometers with more than two paths, and we employ this framework to derive some novel WPDRs.

An interferometer---no matter how clever the design---cannot reveal both the wave and the particle behavior of a quantum system. This fundamental idea has been captured by inequalities, so-called wave-particle duality relations (WPDRs), that upper bound the sum of the fringe visibility (wave behavior) and path distinguishability (particle behavior). Another fundamental idea is Heisenberg's uncertainty principle, stating that some pairs of observables cannot be known simultaneously. Recent work has unified these two principles for two-path interferometers. Here we extend this unification to

n

-path interferometers, showing that WPDRs correspond to a modern formulation of the uncertainty principle stated in terms of entropies. Furthermore, our unification provides a framework for solving an outstanding problem of how to formulate universally valid WPDRs for interferometers with more than two paths, and we employ this framework to derive some novel WPDRs.

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.

A single photon exhibits wave-particle duality in the Young's double-slit interferometer. The duality characterized by an interference visibility and a which-path information has trade-off relation known as complementarity. These quantities are related to the first-order coherence, and the interference is based on the phase correlation between lights coming from two arms. However according to quantum optics theory, such a simple wave-particle picture is not enough to understand the nature because the theory showed an importance of higher-order coherence in the sense of both interference and statistical distribution of photons. Second-order intensity correlation is especially crucial to reveal distinctive quantum features of photons with no classical analogue. Here, in an intensity interferometric scenario as represented by the Hong-Ou-Mandel interferometer, we discuss a wave-particle duality of light based on a which-path information and a quantity characterizing a magnitude of the intensity interferometric effect. We show, for classical light, the two quantities obey the complementary principle similar to the case of the double-slit experiment, but do not for nonclassical light. The nonclassical light such as photons at two arms is allowed to show larger which-path information and intensity interference simultaneously beyond the complementary relation. Moreover, the violation reveals a new nonclassical nature of light although both of the above two quantities seem to be understandable classically, which is never found from a consideration of only one side of wave-particle duality.

The quantification of wave-particle duality (WPD) by means of measurable features associated to it, such as fringe visibility (

\mathcal {V}

) and path distinguishability (

\mathcal {D}

), led to the establishment of the constraint

\mathcal {V}^{2}+\mathcal {D}^{2} \leq \,1

. The two involved quantities refer to so-called "quantons", physical objects that are capable of generating an interferometric pattern, while being at least partially localizable. Any quanton's internal degree of freedom (DOF) can in principle be used as a path-marker. When the quanton and its internal DOF are simultaneously engaged, new constraints can be derived and experimentally tested. Generalized constraints show how

\mathcal {V}

and

\mathcal {D}

relate to other quantifiers and bring to light coherences that might remain otherwise hidden in both quantum and classical light. We submitted two-qubit constraints to experimental tests, using optical light beams. This shows that, despite the rather contrived nature of the constraints, linear optics setups are appropriate to test them. Our experimental results are in very good agreement with theoretical predictions related to the tested constraints. Our results also show that quantifiers such as

\mathcal {V}

and

\mathcal {D}

help not only to quantify, but also to generalize the concept of WPD.

Quantum information tasks are often analyzed under varying trust assumptions about the devices involved. The semi-device-independent (SDI) framework offers a balance between needed assumptions and experimental feasibility. In this work, we study the energy-constrained SDI scenario, where the only assumption in a prepare-and-measure setup is an upper bound on the energy of the prepared quantum states. In contrast to previous studies that restricted the preparation and measurement devices to be classically correlated, we show that allowing entanglement strictly enlarges the set of achievable correlations. We identify two operational consequences of this result. The first concerns randomness certification, where we show that allowing the adversary to employ entangled strategies may significantly reduce the amount of certifiable randomness. This includes situations where the amount of randomness drops to zero in the presence of entanglement, while it remains positive when entanglement is excluded. Second, for the task of distinguishing an arbitrary quantum channel from the identity, we show that the known dimension-independent bound on the advantage conferred by entanglement is violated under an energy constraint.