On September 1, 2011, I posted a partial review of two very interesting papers by G. Chiribella, G. M. D'Ariano, and P. Perinotti attempting to derive finite-dimensional quantum mechanics from physical principles without making purely mathematical assumptions such as that (pure) states are represented by rays in a Hilbert space:
G. Chiribella, G. M. D'Ariano, and P. Perinotti, "Probabilistic theories with purification", Phys. Rev. A 81, 062348 (2010), arXiv:0908,1583
same authors, "Informational derivation of quantum theory", Phys. Rev. A 84, 012311 (2011), arXiv:1011.6451
I want to correct the following erroneous statement in that review:
"Both papers are well written, but in unusual notations invented by the authors, and the notations are different for the two papers. I thought the CDP10 notation was quite successful, but the CDP11 notation less so.
For example, CDP11 uses a thickened horizontal line to denote equality instead of the usual "=", without explicitly informing the readers of this. I found this really puzzling even after I had guessed its meaning. What's wrong with "=", which everybody understands, and why make the reader guess the meaning of unfamiliar symbols?"
The statement was based on the .pdf copy which I obtained from the arXiv and printed. For unknown reasons, it printed as described above, but that is not how the .pdf shows on the screen, and a later reprinting does not have the features described above. In particular, equality is denoted by the usual "=" and not by a thickened horizontal line.
Although there are significant differences in notation and terminology between CDP10 and CDP11, they will probably not bother most readers. I now think that the notation of CDP11 is an improvement over its predecessor.