Native linear-optical protocol for efficient multivariate trace estimation
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914267115028480 |
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| author | Novo, Leonardo Robbio, Marco Galvão, Ernesto F. Cerf, Nicolas J. |
| author_facet | Novo, Leonardo Robbio, Marco Galvão, Ernesto F. Cerf, Nicolas J. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_14204 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Native linear-optical protocol for efficient multivariate trace estimation Novo, Leonardo Robbio, Marco Galvão, Ernesto F. Cerf, Nicolas J. Quantum Physics 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. |
| title | Native linear-optical protocol for efficient multivariate trace estimation |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2601.14204 |