text: 344,144,1326847093886115841,38941661,Daniel Stilck França,"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: <LINK> 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!",https://arxiv.org/abs/2011.05949,"The data processing inequality is the most basic requirement for any meaningful measure of information. It essentially states that distinguishability measures between states decrease if we apply a quantum channel and is the centerpiece of many results in information theory. Moreover, it justifies the operational interpretation of most entropic quantities. In this work, we revisit the notion of contraction coefficients of quantum channels, which provide sharper and specialized versions of the data processing inequality. A concept closely related to data processing is partial orders on quantum channels. First, we discuss several quantum extensions of the well-known less noisy ordering and relate them to contraction coefficients. We further define approximate versions of the partial orders and show how they can give strengthened and conceptually simple proofs of several results on approximating capacities. Moreover, we investigate the relation to other partial orders in the literature and their properties, particularly with regards to tensorization. We then examine the relation between contraction coefficients with other properties of quantum channels such as hypercontractivity. Next, we extend the framework of contraction coefficients to general f-divergences and prove several structural results. Finally, we consider two important classes of quantum channels, namely Weyl-covariant and bosonic Gaussian channels. For those, we determine new contraction coefficients and relations for various partial orders. ","On contraction coefficients, partial orders and approximation of