Unification of coherence and quantum correlations in tripartite systems

In quantum resource theories (QRTs), evidence of intrinsic connections between coherence and quantum correlations, including Bell nonlocality, entanglement, quantum steering, and so on, exists. However, building these relationships is a vital yet challenging task in multipartite quantum systems. Here, we focus on a unified framework of interpreting the interconversions among coherence and different quantum correlations in tripartite systems. In particular, an exact relation between the generalized geometric measure and the genuinely multi -partite concurrence is derived for tripartite entanglement states. Then we obtain the trade-off relation between the first-order coherence and the genuine tripartite entanglement by the genuinely multipartite concurrence and concurrence fill. Furthermore, the trade-off relation between the maximum steering inequality violation and concurrence fill for arbitrary three-qubit states is found. In addition, we investigate the close relation between the maximum steering inequality violation and the first-order coherence. The results show that coherence and quantum correlations are intrinsically related and can be converted to one another in the framework of QRTs.

Automated summary

In this paper, a unified framework for interpreting the interconversions among coherence and different quantum correlations in tripartite systems is proposed. Results include the exact relation between the generalized geometric measure and the genuinely multipartite concurrence for tripartite entanglement states, the trade-off relation between the first-order coherence and the genuine tripartite entanglement, and the trade-off relation between the maximum steering inequality violation and concurrence fill for arbitrary three-qubit states. Additionally, the close relation between the maximum steering inequality violation and the first-order coherence is investigated. The results show that coherence and quantum correlations are intrinsically related and can be converted to one another in the framework of QRTs.