Quantum Doeblin Coefficients: Interpretations and Applications

In classical information theory, the Doeblin coefficient of a classical channel provides an efficiently computable upper bound on the total-variation contraction coefficient of the channel, leading to what is known as a strong data-processing inequality. In this talk, I’ll explain quantum Doeblin coefficients as a generalization of the classical concept. In particular, various new quantum Doeblin coefficients will be defined, one of which has several desirable properties, including concatenation and multiplicativity, in addition to being efficiently computable. Various interpretations of one of the quantum Doeblin coefficients will be developed, including representations as minimal singlet fraction, exclusion value, reverse max-mutual information, reverse robustness, and hypothesis testing reverse mutual information. The interpretations of a quantum Doeblin coefficient as entanglement-assisted exclusion value is particularly appealing, indicating that it is proportional to the best possible error probability one could achieve in an entanglement-assisted state-exclusion task by making use of the channel. I’ll also outline some applications of quantum Doeblin coefficients, including limitations on quantum machine learning algorithms that use parameterized quantum circuits (noise-induced barren plateaus) and on error mitigation protocols. Joint work with Ian George, Christoph Hirche, and Theshani Nuradha. Presented at QUORUM 2025 Meeting (Strathmere, Canada) and 2025 London Symposium on Information Theory (Cambridge, UK).