Quantum direct cause across the Cherenkov threshold in circuit QED

We investigate Cherenkov radiation triggered by qubit acceleration, which can be simulated using superconducting circuits. By analyzing qubit dynamics, we confirm the existence of the Cherenkov speed threshold. A question immediately arises: What is the role of the Cherenkov speed threshold from the aspect of causation? More specifically, what is the effect of the threshold on the ability of the qubit to transmit quantum information? To address this question, we consider measurements of the quantum direct cause, which can be used to estimate channel capacity, based on a recently developed notion on temporal quantum correlations. When choosing proper values for qubit acceleration and qubit-field coupling in a single-mode model, we surprisingly discover that the Cherenkov threshold serves as the speed limit for quantum information propagation in the single-mode model. We further extend use of these measurements to a multimode model. The results indicate that introducing extra modes can lead to further suppression of the quantum direct cause. The suppression is further enhanced when the number of field modes involved in the system is increased.