Efficiently Computable Strategies and Limits for Bosonic Channel Discrimination

Abstract: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.

arXiv:2603.19911 [quant-ph]

(or arXiv:2603.19911v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2603.19911 Focus to learn more arXiv-issued DOI via DataCite

Physical Review A, vol. 114, no. 3, page 032441, September 2026

https://doi.org/10.1103/fypm-kjt6 Focus to learn more DOI(s) linking to related resources

Fig_2_dephasing_function_energy.py

Fig_3_loss_dephasing_function_energy.py

Fig_4_dephasing_function_gamma_E05.py

Fig_6_DA_loss_dephase.py

PermuteSystems.m

RE_loss_dephase_r13.m

RE_lower_dephase_only_r13.m

RE_lower_loss_dephase_r13_v2.m

RE_upper_dephase_only_r13.m

RE_upper_loss_dephase_r13_v2.m

_Content_Types_.xml

bosonic_dephasing_channel.m

bosonic_loss_channel.m

choi_loss_dephasing.m

choi_matrix_bdc.m

choi_matrix_loss.m

choi_matrix_loss_dephase_v2.m

loss_choi_element_2d.m

loss_dephase_choi_element_2d.m

matlab/document.xml

matlab/output.xml

measured_loss_dephase_m3k3_sup_op.m

measured_m3k3_sup_op.m

metadata/coreProperties.xml

metadata/mwcoreProperties.xml

metadata/mwcorePropertiesExtension.xml

primal_ell_8_bdc.m

primal_ell_8_loss_dephase.m

(31 additional files not shown) You must enabled JavaScript to view entire file list.

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.