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# On the Information-Theoretic Structure of Distributed Measurements

On the information-theoretic structure of distributed measurements

David Balduzzi
^{1}^{1}I thank Dominik Janzing, Sanjeevi Krishnan and the reviewers for useful comments.

Max Planck Institute for Intelligent Systems, TÃ¼bingen, Germany

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.

## Collection content

Title | Author | My info |
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1. Introduction | rspuzio | User not logged in |

2. Stochastic maps | rspuzio | User not logged in |

3. Distributed dynamical systems | rspuzio | User not logged in |

4. Measurement | rspuzio | User not logged in |

5. Entanglement | rspuzio | User not logged in |

6. Discussion | rspuzio | User not logged in |

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Added: 2014-04-19 - 20:30