  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 parameter, 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 Horndenski coupling term, as the
modification to standard gravity theory, does not change the qualitative
behaviors of the conductivities and the entanglement measures.
