Heisenberg-scaling characterization of an arbitrary two-channel network via two-port homodyne detection

Quantum Physics [Submitted on 20 Mar 2026] Heisenberg-scaling characterization of an arbitrary two-channel network via two-port homodyne detection Atmadev Rai, Paolo Facchi, Vincenzo Tamma We present a fully Gaussian and experimentally feasible scheme for the simultaneous estimation of the four real parameters that characterize an arbitrary two-channel unitary transformation. The scheme utilizes a two-mode squeezed probe and balanced homodyne detection at both output ports, for which we derive the complete classical Fisher-information matrix analytically. Our scheme achieves the Heisenberg-scaling sensitivity for all four parameters simultaneously, enabling full multiparameter characterization of the generic two-channel interferometric device. We further show, by maximum-likelihood estimation, that the corresponding multiparameter Cramér-Rao bounds are saturated with a modest number of experimental repetitions and for low photon numbers. The scheme establishes a practical route to Heisenberg-scaling multiparameter Gaussian metrology for arbitrary two-channel networks, with direct relevance to calibration and sensing in integrated photonics and distributed quantum-enhanced measurement architectures. Comments: 6 Figures Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.20139 [quant-ph]   (or arXiv:2603.20139v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.20139 Focus to learn more Submission history From: Atmadev Rai [view email] [v1] Fri, 20 Mar 2026 17:11:03 UTC (5,204 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)