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

TL;DR

This paper critically examines a recent claim that the Aharonov-Bohm phase is locally generated by entanglement, and demonstrates that it is fundamentally driven by the vector potential extbf{A}, reaffirming the conventional understanding.

Contribution

The paper refutes the claim that entanglement locally generates the AB phase, clarifies the correct gauge-dependent nature of the phase, and emphasizes the role of the vector potential extbf{A} in its origin.

Findings

The AB phase arises from interaction with the vector potential extbf{A}

The proposed field-based energy formulation is mathematically flawed

The AB phase is gauge-dependent for non-closed paths

Abstract

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.