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 5, 11, 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.)