Fork me on GitHub
Math for the people, by the people.

User login

On the Information-Theoretic Structure of Distributed Measurements

Primary tabs

On the Information-Theoretic Structure of Distributed Measurements

On the information-theoretic structure of distributed measurements

David Balduzzi 11I thank Dominik Janzing, Sanjeevi Krishnan and the reviewers for useful comments.

Max Planck Institute for Intelligent Systems, Tübingen, 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 sectionsPlanetmathPlanetmathPlanetmath of a suitably defined presheafPlanetmathPlanetmath, 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 equivalentPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath to context-dependence. Finally, we show that only indecomposable measurements are more informative than the sum of their submeasurements.

Collection content

Titlesort descendingAuthorMy info
1. IntroductionrspuzioUser not logged in
2. Stochastic mapsrspuzioUser not logged in
3. Distributed dynamical systemsrspuzioUser not logged in
4. MeasurementrspuzioUser not logged in
5. EntanglementrspuzioUser not logged in
6. DiscussionrspuzioUser not logged in

Subscribe to Comments for "On the Information-Theoretic Structure of Distributed Measurements"