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Algorithmic Measurement Procedures

Abstract

Measurements are shown to be processes designed to return figures: they are effective. This effectivity allows for a formalization as Turing machines, which can be described employing computation theory. Inspired in the halting problem we draw some limitations for measurement procedures: procedures that verify if a quantity is measured cannot work in every case.

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Fig. 1

Notes

  1. This calculations, by the way, can be performed without any knowledge of the math beneath them since can be always reduced to the mechanical operations of the machine.

  2. We can add the oracle as a fourth instruction [4].

  3. This is necessary because there are non-repeatable procedures that sometimes measure temperature and sometimes other property but the election is done in a random fashion.

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Acknowledgements

We thank A. Bendersky for his relevant comments. We acknowledge funding from DGAPA- UNAM project IN109417 and IN104020.

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Correspondence to Jorge G. Hirsch.

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Solis-Labastida, A.F.G., Hirsch, J.G. Algorithmic Measurement Procedures. Found Phys 50, 749–763 (2020). https://doi.org/10.1007/s10701-020-00354-4

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Keywords

  • Measurement procedures
  • Algorithmic theory
  • Turing machines