Channel dichotomies

Abstract:We study channel interconversion under non-signalling superchannels, where the asymptotic conversion rate is given by the ratio of the channel capacities. Our main result determines the second-order expansion of the optimal target length. Namely, when each channel has a single capacity-achieving dispersion, the coefficient is given by the inverse sesquinormal distribution, with parameters determined by the capacities and dispersions. The result extends state-dichotomy theory to channels: one superchannel approximates the target uniformly over inputs and maps every reference channel whose output is independent of its input to another such channel. As in state dichotomies, there are finite-error resonances where the second-order term vanishes, leaving an $O(\log n)$ remainder. Crucially, our new characterization cannot be obtained by concatenating channel coding and simulation protocols [Cao {\it et al.}~IEEE Trans.~Inf.~Theory (2024)]. Instead, the proof combines comparisons of binary hypothesis testing experiments with uniform Gaussian estimates and a construction that uses symmetry within type classes to satisfy the non-signalling constraints. Shared randomness assistance already suffices at first order, but we show that its second-order behaviour can differ strictly from the non-signalling case.

Information Theory (cs.IT); Quantum Physics (quant-ph)

arXiv:2610.41858 [cs.IT]

(or arXiv:2610.41858v1 [cs.IT] for this version)

https://doi.org/10.48550/arXiv.2610.41858 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

plot_resonances.py

requirements.txt

verify_near_identity_resonance.py

verify_packet_resonance.py

verify_rate_plots.py

verify_resonance.py

(2 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.