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We find a single parameter family of genuinely entangled three qubit purestates, called the maximally Bell inequality violating states (MBV), whichexhibit maximum Bell inequality violation by the reduced bipartite system for afixed amount of genuine tripartite entanglement quantified by the so calledtangle measure. This in turn implies that there holds a complementary relationbetween the Bell inequality violation by the reduced bipartite systems and thetangle present in the three qubit states, not necessarily pure. The MBV statesalso exhibit maximum Bell inequality violation by the reduced bipartite systemsof the three qubit pure states with a fixed amount of genuine tripartitecorrelation quantified by the generalized geometric measure, a genuineentanglement measure of multiparty pure states, and the discord monogamy score,a multipartite quantum correlation measure from information theoretic paradigm.The aforementioned complementary relation has also been established for threequbit pure states for the generalized geometric measure and the discordmonogamy score respectively. The complementarity between the Bell inequalityviolation by the reduced bipartite systems and the genuine tripartitecorrelation suggests that the Bell inequality violation in the reduced twoqubit system comes at the cost of the total tripartite correlation present inthe entire system.

Complementarity between Tripartite Quantum Correlation and Bipartite Bell Inequality Violation in Three Qubit States