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arXiv · 2601.14204

Native linear-optical protocol for efficient multivariate trace estimation

Leonardo Novo·Marco Robbio·Ernesto F. Galvão·Nicolas J. Cerf
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Abstract

The Hong-Ou-Mandel test estimates the overlap between spectral functions characterizing the internal degrees of freedom of two single photons. It can be viewed as a photon-native protocol that implements the well-known quantum SWAP test. Here, we propose a native linear-optical protocol that efficiently estimates multivariate traces of quantum states called Bargmann invariants, which are ubiquitous in quantum mechanics. Our protocol may be understood as a photon-native version of the cycle test in the circuit model, which encompasses many-photon multimode quantum states. We show the protocol is sample-efficient and discuss applications, such as generalized suppression laws, efficient quantum kernel estimation for quantum machine learning, eigenspectrum estimation, and the characterization of multiphoton indistinguishability.

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Leonardo Novo, Marco Robbio, Ernesto F. Galvão, Nicolas J. Cerf. 2026-01-20. Native linear-optical protocol for efficient multivariate trace estimation. https://arxiv.org/abs/2601.14204

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