Complementary relations of entanglement, coherence, steering and Bell nonlocality inequality violation in three-qubit states

TL;DR

This paper explores fundamental relationships among entanglement, coherence, steering, and Bell nonlocality in three-qubit states, revealing new complementary relations and connections between these quantum properties.

Contribution

It introduces new complementary relations among key quantum correlations in three-qubit states and establishes links between negativity and various nonlocality measures.

Findings

Negativity equals the geometric mean of bipartite concurrences for pure states.

Maximum coherence and steering violation are achieved at fixed negativity.

Negativity relates closely to maximum steering and Bell inequality violations.

Abstract

We put forward complementary relations of entanglement, coherence, steering inequality violation, and Bell nonlocality for arbitrary three-qubit states. We show that two families of genuinely entangled three-qubit pure states with single parameter exist, and they exhibit maximum coherence and steering inequality violation for a fixed amount of negativity, respectively. It is found that the negativity is exactly equal to the geometric mean of bipartite concurrences for the three-qubit pure states, although the negativity is always less than or equal to the latter for three-qubit mixed states. Moreover, the complementary relation between negativity and first-order coherence for tripartite entanglement states are established. Furthermore, we investigate the close relation between the negativity and the maximum steering inequality violation. In addition, the complementary relation between negativity and the maximum Bell-inequality violation for arbitrary three-qubit states is obtained. The results provide reliable evidence of fundamental connections among entanglement, coherence, steering inequality violation, and Bell nonlocality.