Efficiently Computable Strategies and Limits for Bosonic Channel Discrimination

Quantum Physics [Submitted on 20 Mar 2026] Efficiently Computable Strategies and Limits for Bosonic Channel Discrimination Zixin Huang, Ludovico Lami, Vishal Singh, Mark M. Wilde Discriminating between noisy quantum processes is a central primitive for quantum communication, metrology, and computing. While discrimination limits for finite-dimensional channels are well understood, the continuous-variable setting, particularly under experimentally relevant energy constraints, remains significantly less developed. In this work, we establish an energy-constrained chain rule for the Belavkin-Staszewski channel divergence, which yields a fundamental upper bound on the error exponents achievable by fully adaptive, energy-constrained quantum channel discrimination protocols. We then derive efficiently computable bounds on asymmetric error exponents for energy-constrained discrimination of bosonic dephasing and loss-dephasing channels. Specifically, we show that three operationally relevant quantities -- the measured relative entropy, the Umegaki relative entropy, and the geometric Renyi divergence -- admit semidefinite program (SDP) formulations when the input energy is bounded and the Hilbert space is suitably truncated. Applying these tools, we demonstrate that optimal probes for these channels under energy constraints are Fock-diagonal, and we also enable numerically precise evaluation of bounds on achievable error exponents across discrimination strategies ranging from separable to fully adaptive. The resulting SDPs provide practical benchmarks for quantum-limited sensing in low-energy bosonic platforms. Comments: 7 pages, 5 figures and 20 pages of appendices Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.19911 [quant-ph]   (or arXiv:2603.19911v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.19911 Focus to learn more Submission history From: Zixin Huang [view email] [v1] Fri, 20 Mar 2026 12:50:35 UTC (377 KB) Access Paper: HTML (experimental) view license Ancillary files (details): Fig_2_dephasing_function_energy.py Fig_3_loss_dephasing_function_energy.py Fig_4_dephasing_function_gamma_E05.py Fig_5_DA.py Fig_6_DA_loss_dephase.py (31 additional files not shown) 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?)