On the information-theoretic structure of distributed measurements

David Balduzzi
(MPI for Intelligent Systems)

The internal structure of a measuring device, which depends on what its components are and how they are organized, determines how it categorizes its inputs. This paper presents a geometric approach to studying the internal structure of measurements performed by distributed systems such as probabilistic cellular automata. It constructs the quale, a family of sections of a suitably defined presheaf, whose elements correspond to the measurements performed by all subsystems of a distributed system. Using the quale we quantify (i) the information generated by a measurement; (ii) the extent to which a measurement is context-dependent; and (iii) whether a measurement is decomposable into independent submeasurements, which turns out to be equivalent to context-dependence. Finally, we show that only indecomposable measurements are more informative than the sum of their submeasurements.

In Elham Kashefi, Jean Krivine and Femke van Raamsdonk: Proceedings 7th International Workshop on Developments of Computational Methods (DCM 2011), Zurich, Switzerland, 3rd July 2011, Electronic Proceedings in Theoretical Computer Science 88, pp. 28–42.
Published: 30th July 2012.

ArXived at: http://dx.doi.org/10.4204/EPTCS.88.3 bibtex PDF
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