Correlated Knowledge: an Epistemic-Logic View on Quantum Entanglement

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