Violation of Bell’s inequalities by continuous probing of a two-qubit system

We theoretically analyze the Bell’s inequalities by continuously monitoring a system comprising two-coupled superconducting qubits. The weak probing could measure the observables accurately after sufficient runs. While for the strong measurement, due to the measurement backaction, the system will collapse to the basis state corresponding to the eigenvalue measured with a higher probability. Interestingly, for system in the maximal two-qubit entanglement state, the measurement backaction from strong probe could be compensated by a parity measurement. Under the imperfect detection, a correction term could help yield a result which is compatible with the correct value of the observables. Furthermore, we investigate the Bell’s inequalities during the dynamical evolution of the coupled two-qubit system and demonstrate that the more the two-qubit entangle, the larger violation of Bell’s inequality will present with the upper bound $$2\sqrt{2}$$ .