A Proof of Everett's Correlation Conjecture.

August 2010

Abstract In his long 1957 paper “The Theory of the Universal Wave Function” (discussed here), Hugh Everett III made some significant preliminary steps towards the application and generalization of Shannon's information theory to quantum mechanics. In the course of doing so he conjectured that, for a given wavefunction on a compound space, the Schmidt decomposition maximises the correlation between subsystem bases. I show how this conjecture can be proved as an application of the strong subadditivity of quantum entropy.

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Matthew J. Donald

The Cavendish Laboratory, JJ Thomson Avenue, Cambridge CB3 0HE, Great Britain.

e-mail : mjd1014@cam.ac.uk

home page: http://people.bss.phy.cam.ac.uk/~mjd1014