  We investigate the Cherenkov radiation triggered by qubit acceleration
simulated by superconducting circuit. By analyzing the radiation probability,
we confirm the existence of Cherenkov speed threshold, implying that simulating
superluminal qubit motion is possible for such a scenario. A question
immediately arises: Is such motion compatible with the causality principle? To
address the question, we perform a causality test on the simulating system
based on the recently developed notion of temporal quantum correlations,
pseudo-density matrix and temporal quantum steering. The results suggest that
single-mode approximation breaks down even when the system is restricted in
weak coupling regime.
