There is no axiom central to empiricism, since empiricism relies on proof, whereas axioms are accepted as true without any. The purpose and fundamental core of empiricism is to be free from axiom, and to question and test everything.
Entangled particles and wave functions are physical phenomena, contrary to what you have claimed, because they a) exist in nature, b) possess energy and c) have measurable, predictable effects. This classification of (a seemingly arbitrarily-chosen pair of) quantum phenomena is not axiomatic because it does not rely on faith to proceed, it is a simple definition of terms, used to agree what is a physical phenomenon.
We do not need faith to measure quantum entanglement, we need an experimental setup.
We do not need faith to describe the wave function, we need Schrödinger’s equation. So I will call empiricism what it is: deriving objective truth through observation, deduction and consensus using the scientific method.
Empiricism is not concerned with subjective truth, because subjective truth, whilst important to lived experience, is unimportant in the purely pragmatic furthering of the progress of human understanding of the physical universe. Again, this is not axiomatic, just a definition of terms.