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arXiv:2601.10289

Exponential improvement in benchmarking multiphoton interference

Rodrigo M. Sanz, Emilio Annoni, Stephen C. Wein, Carmen G. Almudever, Shane Mansfield, Ellen Derbyshire, Rawad Mezher

quant-phSubmitted Jan 15, 2026• Announced Jan 16, 2026• 0 citations
arXivHTMLPDF

Abstract

Several photonic quantum technologies rely on the ability to generate multiple indistinguishable photons. Benchmarking the level of indistinguishability of these photons is essential for scalability. The Hong-Ou-Mandel dip provides a benchmark for the indistinguishability between two photons, and extending this test to the multi-photon setting has so far resulted in a protocol that computes the genuine n-photon indistinguishability (GI). However, this protocol has a sample complexity that increases exponentially with the number of input photons for an estimation of GI up to a given additive error. To address this problem, we introduce new theorems that strengthen our understanding of the relationship between distinguishability and the suppression laws of the quantum Fourier transform interferometer (QFT). Building on this, we propose a protocol using the QFT for benchmarking GI that achieves constant sample complexity for the estimation of GI up to a given additive error for prime photon numbers, and sub-polynomial scaling otherwise, representing an exponential improvement over the state of the art. We prove the optimality of our protocol in many relevant scenarios and validate our approach experimentally on Quandela's reconfigurable photonic quantum processor, where we observe a clear advantage in runtime and precision over the state of the art. We therefore establish the first scalable method for computing multi-photon indistinguishability, which applies naturally to current and near-term photonic quantum hardware.

Comments
7 pages + 20 pages appendix, comments welcome !

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Several photonic quantum technologies rely on the ability to generate multiple indistinguishable photons. Benchmarking the level of indistinguishability of these photons is essential for scalability. The Hong-Ou-Mandel dip provides a benchmark for the indistinguishability between two photons, and extending this test to the multi-photon setting has so far resulted in a protocol that computes the genuine n-photon indistinguishability (GI). However, this protocol has a sample complexity that increases exponentially with the number of input photons for an estimation of GI up to a given additive error. To address this problem, we introduce new theorems that strengthen our understanding of the relationship between distinguishability and the suppression laws of the quantum Fourier transform interferometer (QFT). Building on this, we propose a protocol using the QFT for benchmarking GI that achieves constant sample complexity for the estimation of GI up to a given additive error for prime photon numbers, and sub-polynomial scaling otherwise, representing an exponential improvement over the state of the art. We prove the optimality of our protocol in many relevant scenarios and validate our approach experimentally on Quandela's reconfigurable photonic quantum processor, where we observe a clear advantage in runtime and precision over the state of the art. We therefore establish the first scalable method for computing multi-photon indistinguishability, which applies naturally to current and near-term photonic quantum hardware.
Multiphoton indistinguishability is a key resource for photonic quantum technologies, yet its characterization typically relies on resource-intensive methods. In this work, we develop two efficient and experimentally friendly protocols to estimate or bound the fidelity FindF_{\mathrm{ind}}Find​ of an NNN-photon state to the closest perfectly indistinguishable state. The first protocol applies to sources preparing separable states, uses a single Fourier interferometer together with photon-number-resolving detection, and yields tight two-sided bounds on FindF_{\mathrm{ind}}Find​. The second protocol combines randomized implementations of linear-optical interferometers with photon counting, enabling direct estimation of FindF_{\mathrm{ind}}Find​ for arbitrary NNN-photon states. Both protocols can certify Find=1−O(ε)F_{\mathrm{ind}} = 1 - \mathcal{O}(ε)Find​=1−O(ε) using provably optimal O(1/ε)\mathcal{O}(1/ε)O(1/ε) samples, in contrast to previous approaches which required prior assumptions on the model of partial distinguishability. Our methods, based on a multiphoton generalization of the Hong-Ou-Mandel test, bring the rigorous and operationally meaningful certification of multiphoton indistinguishability within reach of current photonic technologies.
Multiphoton interference represents one of the key features in photonic platforms for quantum communication, quantum simulation, quantum computing and quantum sensing. Starting from the first two-photon experiment by Hong-Ou-Mandel [1], it has been shown that multiphoton interference lies at the heart of computational complexity in linear optical interferometers, the most notable example being provided by the Boson Sampling model [2]. This model corresponds to sampling from the evolution of n indistinguishable photons in a multimode linear network, and has been shown to be hard to simulate classicaly thus representing a promising route to experimentally reach the quantum advantage regime. It has been shown, however, that genuine multiparticle interference is necessary for high computational complexity. Hence, appropriate methods for detection of such feature should be developed since the complexity of problem prevents the application of trivial methods.
The generation of quantum states of many indistinguishable photons is a crucial resource for the realization of photonic computer architectures that can enable a quantum speedup and create fault-tolerant multi-party quantum networks. On the experimental side, the measurement of indistinguishability for a multi-photon state is a challenging task. In the case of a two-photon state, the photon indistinguishability is fully assessed by the visibility of the interference fringe of the Hong-Ou-Mandel (HOM) interference experiment on a balanced beam splitter. However, pairwise HOM experiments are unable to completely determine the multi-photon indistinguishability when more than two photons are involved [1]–[2].
Particle indistinguishability is at the heart of quantum statistics that regulates fundamental phenomena such as the electronic band structure of solids, Bose-Einstein condensation and superconductivity. Moreover, it is necessary in practical applications such as linear optical quantum computation and simulation, in particular for Boson Sampling devices. It is thus crucial to develop tools to certify genuine multiphoton interference between multiple sources. Our approach employs the total variation distance to find those transformations that minimize the error probability in discriminating the behaviors of distinguishable and indistinguishable photons. In particular, we show that so-called Sylvester interferometers are near-optimal for this task. By using Bayesian tests and inference, we numerically show that Sylvester transformations largely outperform most Haar-random unitaries in terms of sample size required. Furthermore, we experimentally demonstrate the efficacy of the transformation using an efficient 3D integrated circuits in the single- and multiple-source cases. We then discuss the extension of this approach to a larger number of photons and modes. These results open the way to the application of Sylvester interferometers for optimal assessment of multiphoton interference experiments.
This thesis presents the development of resource-efficient photon-distillation schemes designed to produce highly indistinguishable photons, a key requirement for large-scale photonic quantum computing. Although photons do not naturally interact, their indistinguishability enables effective interactions through quantum interference, allowing entanglement generation using only linear optical elements and measurements. In practice, however, photons are never perfectly identical. Small differences introduce decoherence, limiting the scalability and reliability of photonic quantum technologies. Addressing indistinguishability errors is therefore essential for fault-tolerant quantum computing. The thesis first reviews the importance of photon indistinguishability and the need to mitigate related errors. It then examines experimental methods for characterizing imperfections and introduces a general model of imperfect photon states. This model captures indistinguishability errors alongside additional experimental noise from photon loss and multiphoton events. A key insight is that loss and multiphoton noise together can act as an effective source of indistinguishability error. To quantify this effect, the work defines an effective indistinguishability metric, enabling practical evaluation of photon-distillation schemes under realistic conditions. The core theoretical contribution is the development of photon-distillation protocols based on multiphoton Fourier interference. Unlike earlier approaches, these schemes can asymptotically suppress indistinguishability errors to arbitrary levels while requiring only linear scaling in photon resources relative to the desired error reduction. The analysis further suggests that photon distillation, when combined with quantum error correction, can significantly reduce the overall resource overhead for fault-tolerant photonic quantum computing. Experimentally, a three-photon Fourier-based distillation protocol was demonstrated on a high-fidelity photonic processor using a resonantly driven quantum-dot single-photon source. After subtracting excess noise contributions, a 2.2-fold reduction in indistinguishability error was achieved; when excess noise was retained, a 1.2-fold net reduction was observed. These results confirm a clear below-threshold improvement in photon quality. Additional analysis suggests that optimized distillation schemes could reduce the photon cost of a logical qubit by up to a factor of four. The thesis concludes by addressing insertion loss and outlining design strategies and future directions for integrating photon-distillation components into scalable quantum architectures.
The investigation of multi-photon quantum interference in symmetric multi-port splitters has both fundamental and applicative interest. Destructive quantum interference in devices with specific symmetry leads to the suppression of a large number of possible output states, generalizing the Hong-Ou-Mandel effect; simple suppression laws have been developed for interferometers implementing the Fourier or the Hadamard transform over the modes. In fact, these enhanced interference features in the output distribution can be used to assess the indistinguishability of single-photon sources, and symmetric interferometers have been envisaged as benchmark or validation devices for Boson-Sampling machines. In this work we devise an innovative approach to implement symmetric multi-mode interferometers that realize the Fourier and Hadamard transform over the optical modes, exploiting integrated waveguide circuits. Our design is based on the optical implementations of the Fast-Fourier and Fast-Hadamard transform algorithms, and exploits a novel three-dimensional layout which is made possible by the unique capabilities of femtosecond laser waveguide writing. We fabricate devices with m = 4 and m = 8 modes and we let two identical photons evolve in the circuit. By characterizing the coincidence output distribution we are able to observe experimentally the known suppression laws for the output states. In particular, we characterize the robustness of this approach to assess the photons' indistinguishability and to rule out alternative non-quantum states of light. The reported results pave the way to the adoption of symmetric multiport interferometers as pivotal tools in the diagnostics and certification of quantum photonic platforms.