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

We find a single parameter family of genuinely entangled three qubit pure states, called maximally Bell inequality violating states, which exhibits maximum Bell inequality violation by the reduced bipartite system for a fixed amount of genuine tripartite correlation. This in turn implies that there holds a complementary relation between the Bell inequality violation by the reduced bipartite systems and the genuine tripartite correlation present in the tripartite pure states. Tangle, generalized geometric measure of entanglement and discord monogamy score have been considered to quantify the genuine quantum correlation of the tripartite pure states. The complementarity between Bell inequality violation by the reduced bipartite systems and the genuine tripartite correlation suggests that the Bell inequality violation in the reduced two qubit system comes at the cost of the total tripartite correlation present in the entire system.