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Topic: Correction to review of Chiribella, et al.'s derivation of quantum

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Stephen Parrott

Posts: 3
Registered: 9/2/11
Correction to review of Chiribella, et al.'s derivation of quantum

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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