text:   capacities for quantum channels",10,"['New paper out with the great @ChristophHirche and Cambyse Rouzé: On contraction coefficients, partial orders and approximation of capacities for quantum channels (<LINK>). See 👇 for a summary!', 'as indicated by the title, we talk about three intertwined subjects: contraction coefficients, partial orders for channels and capacities. Roughly speaking, contraction coefficients quantify by how much a channel makes states indistinguishable.', 'Partial orders try to capture the notion that one channel is noisier than the other, while capacities quantify how useful a channel is for a task in the limit of many uses. Let us now discuss what we add to the discussion:', 'As usual, tensorization is a huge issue for all these themes. We define some new orders for channels that tensorize and show new relations amongst existing ones. This figure summarizes all relations: https://t.co/lmkWENU5wZ', 'We then put epsilons around all these orderings. This leads to new capacity bounds. Also, using our new orderings, we get simple, transparent proofs of the bounds based on approximate degradability by Sutter et al.', 'Most of these orderings, like less noisy, are based on a bound on the mutual information of the output of the channels. We then proceed to show that one can equivalently formulate them in terms of a strong data processing inequality. This leads us to contraction coefficients.', 'Here we study new ways to obtain strict contractions, with a focus on the relative entropy. We discuss a hypercontractive approach combined with the Petz recovery map.', 'We also get new results for Weyl-covariant channels and compute the contraction coefficients for important classes of Gaussian channels. Finally, we extend our results to f-divergences and discuss how the contraction coefficients for various divergences are related.', 'Now, some personal comments. I was really happy to finally write a paper with @ChristophHirche! We met at a spring school 7 years ago when we were still bachelor students, so it was time for this to happen!', 'And I am also happy to continue my fruitful collaboration with Cambyse, as after this paper he is now my most frequent collaborator!']",20,11,2134