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

• URL: http://arxiv.org/abs/2212.09326v2
• Date: Sat, 29 Apr 2023 00:32:51 GMT
• Title: Complementary relations of entanglement, coherence, steering and Bell nonlocality inequality violation in three-qubit states
• Authors: Dong-Dong Dong, Xue-Ke Song, Xiao-Gang Fan, Liu Ye, and Dong Wang
• Abstract summary: We put forward complementary relations of entanglement, coherence, steering inequality violation, and Bell nonlocality for arbitrary three-qubit states. The results provide reliable evidence of fundamental connections among entanglement, coherence, steering inequality violation, and Bell nonlocality.
• Score: 4.8723490038152635
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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