As a general rule, whenever I am informed of typos or mistakes, I will fix them and update the arXiv version of the paper if 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.
- In Theorem 5.13., the conditional entropies should be sandwiched (tildes are missing). On the other hand, the two cases are determined by the sign of (\alpha −1)(\beta −1)(\gamma −1) , which fixes a typo in the original work by Dupuis.

**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.

**Correlation Detection and an Operational Interpretation of the Renyi Mutual Information** – Journal of Mathematical Physics 57, 102201 (with Masahito Hayashi)

The erratum is relative to the current arXiv version: 1408.6894

In Lemmas 22 and 23 the range of validity for \alpha should exclude \alpha = \frac12 and thus read \alpha \in (\frac12, 1) . Indeed, the statements as presented are wrong in this case. The case of \alpha = \frac12 has received more attention in https://arxiv.org/abs/2211.12804. (We thank Laura Burri and Roberto Rubboli for pointing out this issue.)