Optimal filtering for a giant cavity in waveguide QED systems

Quantum Physics [Submitted on 24 Mar 2026] Optimal filtering for a giant cavity in waveguide QED systems Guangpu Wu, Shibei Xue, Yuting Zhu, Guofeng Zhang, Ian R. Petersen In waveguide quantum electrodynamics (QED) systems, a giant cavity can be engineered to interact with quantum fields by multiple distant coupling points so that its non-Markovian dynamics are quite different from traditional quantum optical cavity systems. Towards feedback control this system, this paper designs an optimal filter for the giant cavity systems to estimate its state evolution under continuous quantum measurements. Firstly, the Langevin equation in the Heisenberg picture are derived, which is a linear continuous-time system with both states and inputs delays resulting from the unconventional distant couplings. Compared to existing modeling approaches, this formulation effectively preserves the nonlocal coupling and multiple delay dynamic characteristics inherent in the original system. In particular, the presence of coupling and propagation delays leads to noncommutativity among the system operators at different times, which prevents the direct application of existing quantum filtering methods. To address this issue, an optimal filter is designed, in which the delayed-state covariance matrices are computed. By iteratively evaluating the delayed-state covariance over successive time intervals, the resulting optimal filter can be implemented in an interval-wise backward recursion algorithm. Finally, numerical simulations are conducted to evaluate the tracking performance of the proposed optimal filter for the giant cavity. By comparing between the evolutions of Wigner functions of coherent and cat states and the filter, the effectiveness of the optimal filter is validated. Comments: 11 pages, 4 figures Subjects: Quantum Physics (quant-ph); Systems and Control (eess.SY) Cite as: arXiv:2603.22710 [quant-ph]   (or arXiv:2603.22710v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.22710 Focus to learn more Submission history From: Shibei Xue [view email] [v1] Tue, 24 Mar 2026 02:02:41 UTC (3,190 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 Change to browse by: cs cs.SY eess eess.SY 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?)