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

Abstract

We find a single parameter family of genuinely entangled three qubit pure states, called the maximally Bell inequality violating states (MBV), which exhibit maximum Bell inequality violation by the reduced bipartite system for a fixed amount of genuine tripartite entanglement quantified by the so called tangle measure. This in turn implies that there holds a complementary relation between the Bell inequality violation by the reduced bipartite systems and the tangle present in the three qubit states, not necessarily pure. The MBV states also exhibit maximum Bell inequality violation by the reduced bipartite systems of the three qubit pure states with a fixed amount of genuine tripartite correlation quantified by the generalized geometric measure, a genuine entanglement 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 three qubit pure states for the generalized geometric measure and the discord monogamy score respectively. The complementarity between the 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.

13 pages, 3 figures; New results added for mixed states, presentation changed accordingly, accepted in Physical Review A

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• Unification of quantum resources in tripartite systems
• Entanglement Dynamics for Two Spins in an Optical Cavity---Field Interaction Induced Decoherence and Coherence Revival
• Complementarity of genuine multipartite non-locality
• Trade-off relations of l_1-norm coherence for multipartite systems
• Note on Product-Form Monogamy Relations for Nonlocality and Other Correlation Measures
• Maximal Secret Reconstruction, Teleportation and Bell's Inequality
• Several Trade off Features of Quantum Steering in Distributed Scenario
• Emergence of Monogamy under Static and Dynamic Scenarios
• Trade-off relations on CHSH tests for multi-qubit pure states