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Correction to review of Chiribella, et al.'s derivation of quantum mechanics
Posted:
Oct 31, 2011 1:30 PM


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 finitedimensional 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.
Stephen Parrott



