Proposal for locality test of Aharonov-Bohm effect via Andreev interferometer without a loop. (arXiv:1512.02765v3 [quant-ph] UPDATED)

We propose a quantitative test of the quantum nonlocality in the
electromagnetic interaction that generates the Aharonov-Bohm effect. For this
purpose, we derive an interaction Lagrangian based on the local action of
gauge-invariant quantities only, and compare it with the standard
potential-based ("nonlocal") Lagrangian. It is shown that the two models
provide identical results for any phenomena involving classical equations of
motion or topological quantum phases. Interestingly, we find an example
violating this equivalence, that is, the interference of single charges
coproduced from two independent sources. Whereas a well-defined phase shift of
the interference is predicted in the "local" model, the standard nonlocal
Lagrangian does not provide a gauge-invariant phase shift. This implies that an
observation of the interference in the proposed setup can rule out the
gauge-dependent potential-based model. This result has profound implications as
it can settle the issue of dynamical nonlocality in the quantum electromagnetic
interaction.

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