Mixed-state Entanglement and Transport in Einstein–Maxwell–Axion–Horndeski Theory

We present a comprehensive study exploring the relationship between transport properties and measures of quantum entanglement in the Einstein–Maxwell–Axion–Horndeski theory. By using holographic duality, we study the entanglement measures, holographic entanglement entropy (HEE) and entanglement wedge cross-section (EWCS), and transport coefficients, for this model and analyze their dependence on free parameters which we classify into action parameters, observable parameters and axion factor. We find contrasting behaviors between HEE and EWCS with respect to observable parameters (charge and temperature), and the axion factor, indicating that they capture different types of quantum correlations. We also find that HEE exhibits positive correlation with both charge and thermal excitations, whereas EWCS exhibits a negative correlation with charge-related conductivities and thermal fluctuations. Furthermore, we find that the Horndeski coupling term, as the modification to standard gravity theory, does not change the qualitative behaviors of the conductivities and the entanglement measures.