  Consider four binary +-1 variables A, B, C and D for which classical
reasoning implies ABCD = 1. In this case the knowledge of A, B, C automatically
provides knowledge of D because D = ABC. However, the
Greenberger-Horne-Zeilinger paradox shows that despite classical prediction one
can find quantum states and observables with well defined outcomes for which D
= -ABC. In this work we formulate an information-theoretic version of this
paradox. We show that for a tripartite quantum system one can find a set of
four properties for which classical reasoning implies that D = ABC, yet quantum
theory predicts that one can know everything about A, B, C and nothing about D.
