Native linear-optical protocol for efficient multivariate trace estimation

• URL: http://arxiv.org/abs/2601.14204v1
• Date: Tue, 20 Jan 2026 18:07:27 GMT
• Title: Native linear-optical protocol for efficient multivariate trace estimation
• Authors: Leonardo Novo, Marco Robbio, Ernesto F. Galvão, Nicolas J. Cerf,
• Abstract summary: We propose a native linear-optical protocol that efficiently estimates multivariate traces of quantum states called Bargmann invariants.<n>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.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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