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