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arXiv · 2606.19730

Topological Quantum Interferometry

Tianyou Ying·Yufeng Zhou·Chengwei Pan·Ryan Hogan·Ruoyang Zhang·Hui Liu·Shining Zhu·Xiaoqin Gao
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Abstract

Structured light provides high-dimensional Hilbert spaces holding tremendous potential for fundamental quantum optics and quantum technologies. However, existing characterization methods, like Hong-Ou-Mandel (HOM) interference, typically assume perfectly tuned conditions, overlooking the geometric physics governing spatial mode evolution. Here, we establish topological quantum interferometry driven by an interaction-based geometric phase, the exchange Berry phase (BPX). Our formalism generalizes $q$-plate state generation and characterization to arbitrary topological charges and (de)tuning conditions, demonstrating that BPX acts as a geometric marker governing spatial interference. We show BPX serves as a deterministic control parameter, decomposing two-photon spatial patterns into geometry-dictated fundamental modes. This mapping reveals topological invariants and phase singularities that function as a non-tomographic witness for state dimensionality estimation, circumventing full-state reconstruction. Being device-independent and highly scalable, this approach enables scalable high-dimensional characterization and topologically protected state selection, with direct applicability to quantum metrology and high-capacity quantum networks.

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Tianyou Ying, Yufeng Zhou, Chengwei Pan, Ryan Hogan, Ruoyang Zhang, Hui Liu, Shining Zhu, Xiaoqin Gao. 2026-06-18. Topological Quantum Interferometry. https://arxiv.org/abs/2606.19730

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