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International Journal of Theoretical Physics

, Volume 49, Issue 12, pp 3005–3021 | Cite as

Correlated Knowledge: an Epistemic-Logic View on Quantum Entanglement

  • Alexandru Baltag
  • Sonja Smets
Open Access
Article

Abstract

In this paper we give a logical analysis of both classical and quantum correlations. We propose a new logical system to reason about the information carried by a complex system composed of several parts. Our formalism is based on an extension of epistemic logic with operators for “group knowledge” (the logic GEL), further extended with atomic sentences describing the results of “joint observations” (the logic LCK). As models we introduce correlation models, as a generalization of the standard representation of epistemic models as vector models. We give sound and complete axiomatizations for our logics, and we use this setting to investigate the relationship between the information carried by each of the parts of a complex system and the information carried by the whole system. In particular we distinguish between the “distributed information”, obtainable by simply pooling together all the information that can be separately observed in any of the parts, and “correlated information”, obtainable only by doing joint observations of the parts (and pooling together the results). Our formalism throws a new light on the difference between classical and quantum information and gives rise to an informational-logical characterization of the notion of “quantum entanglement”.

Keywords

Logics for quantum information Quantum correlations Entanglement Correlation models Epistemic logic Correlated knowledge 

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Copyright information

© The Author(s) 2010

Authors and Affiliations

  1. 1.Computing LaboratoryOxford UniversityOxfordUK
  2. 2.Dept. of Artificial Intelligence and Dept. of PhilosophyUniversity of GroningenGroningenNetherlands
  3. 3.IEGOxford UniversityOxfordUK

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