As a general rule, whenever I am informed of typos or mistakes, I will fix them and update the arXiv version of the paper when needed. Hence, this should be the first place to check if you are unsure about an issue in a published paper.

**Quantum Information Processing with Finite Resources** – Monograph (Springer)

The errata are relative to the current arXiv version: 1504.00233

- In Section 4.1.1., Axiom I on continuity: Continuity is actually only ensured when both \rho \ll \sigma and \sigma \ll \rho , that is, wherever the supports of the two states coincide. I thank Omar Fawzi for pointing out this mistake.
- A proof of this continuity is currently missing in the book. Please check out the lecture notes on the Masterclass on Entropy Inequalities instead.

**Quantum Markov chains and logarithmic trace inequalities** – Proc. IEEE ISIT 2017 (with David Sutter and Mario Berta)

*Proposition IV.1* is incorrect. The problem in the proof is that after Eq. (16) we choose ω as a function of t; however, it should be independent of it. We have since found numerical evidence that the statement of the Proposition is in fact incorrect.