Comment on "Aharonov-Bohm Phase is Locally Generated Like All Other Quantum Phases"

Marletto and Vedral [Phys. Rev. Lett. 125, 040401 (2020)] propose that the Aharonov-Bohm (AB) phase is locally mediated by entanglement between a charged particle and the quantized electromagnetic field, asserting gauge independence for non-closed paths. In this Comment, we critically analyze their model and demonstrate that the AB phase arises from the interaction with the vector potential $\mathbf{A}$, not from entanglement, which is a byproduct of the quantum electrodynamics (QED) framework. We show that their field-based energy formulation, intended to reflect local electromagnetic interactions, is mathematically flawed due to an incorrect prefactor and yields $+q \mathbf{v} \cdot \mathbf{A}_{\mathbf{s}}$ in the Coulomb gauge, conflicting with QED's $-q \mathbf{v} \cdot \mathbf{A}_{\mathbf{s}}$. This equivalence to $q \mathbf{v} \cdot \mathbf{A}_{\mathbf{s}}$ holds only approximately in the Coulomb gauge under static conditions, failing for time-dependent fields and other gauges, undermining their claim of a gauge-independent local mechanism. Furthermore, we confirm that the AB phase is gauge-dependent for non-closed paths, contradicting their assertion. Our analysis reaffirms the conventional explanation in the semi-classical picture, where the AB phase is driven by the vector potential $\mathbf{A}$, with entanglement playing no causal role in its generation.