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

TL;DR

This paper identifies a family of three-qubit states that maximizes bipartite Bell inequality violation for a given level of tripartite entanglement, revealing a fundamental complementarity between bipartite nonlocality and tripartite correlations.

Contribution

It introduces the maximally Bell inequality violating (MBV) states and establishes a quantitative complementarity between bipartite Bell violation and tripartite entanglement measures in three-qubit states.

Findings

MBV states exhibit maximum Bell violation for fixed tripartite entanglement.

A complementary relation exists between bipartite Bell violation and tripartite correlations.

The relation holds for various tripartite entanglement measures.

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.