I Incompleteness of Griffiths' consistent histories interpretation

[gentzen]

what I am concerned with is singling out he use of real numbers (which complex number rely of also of course). This is a problem if you consider the IGUS to have limited capacity, or a bound. Then how can such a IGUS represent the continuum? This - for me - is a bigger problem. I expect the continuum model, to be a limiting case of when a LARGE IGUS describes a small system.

The limit is rather the assumption of a state that can be "reproduced arbitrarily often". If you go to the description of bigger and bigger systems, then this assumption becomes more and more ridiculous. So the size of the IGUS is less problematic than the size of the system it tries to describe.

CH doesn't seem well suited for studying such accuracy issues. The information based interpretations (and also the thermal interpretation) are better suited for that. For example, Scott also points out in his post an exponential accuracy issue with using correlations between classical measurement results for measuring nonlocal states. (And this issue translates into that the state preparation and measurements have to be repeated ridiculously often.) Quantum memory could provide an exponential advantage here, but I once raised doubts whether preparation procedures are really as accurately repeatable as required for such results.