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We present a comprehensive study exploring the relationship between transportproperties and measures of quantum entanglement in theEinstein-Maxwell-Axion-Horndeski theory. By using holographic duality, we studythe entanglement measures, holographic entanglement entropy (HEE) andentanglement wedge cross-section (EWCS), and transport coefficients, for thismodel and analyze their dependence on free parameters which we classify intoaction parameter, observable parameters and axion factor. We find contrastingbehaviors between HEE and EWCS with respect to observable parameters (chargeand temperature), and the axion factor, indicating that they capture differenttypes of quantum correlations. We also find that HEE exhibits positivecorrelation with both charge and thermal excitations, whereas EWCS exhibits anegative correlation with charge-related conductivities and thermalfluctuations. Furthermore, we find that the Horndenski coupling term, as themodification to standard gravity theory, does not change the qualitativebehaviors of the conductivities and the entanglement measures.

Mixed-State Entanglement and Transport in Einstein-Maxwell-Axion-Horndeski Theory