Correction to review of Chiribella, et al.'s derivation of quantummechanics

Discussion in 'Math Research' started by Stephen Parrott, Oct 31, 2011.

  1. 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
    Stephen Parrott, Oct 31, 2011
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