Quantum correlations of coupled superconducting two-qubit system in various cavity environments

• We investigate dynamic evolutions of quantum and classical correlations for coupled superconducting system with various cavity environments.
• We show that the quantum discord continues to reflect quantum information.
• A transition of quantum discord is founded between classical loss and quantum increasing of correlations for a purely dephasing mode.
• We show that the environment-dependent models can delay the loss of quantum discord.
• We find that the results depend strongly on the initial angle.

Dynamic evolutions of quantum discord, concurrence, and classical correlation are investigated in coupled superconducting system with various cavity environments, focusing on the two-qubit system at an initially entangling X-state and Y-state. We find that for a smaller photon number, the quantum discord, concurrence and classical correlation show damped oscillations for all different decay modes. Differently from the sudden death or the dark and bright periods emerging in evolving processing of the concurrence and classical correlation, however, the quantum discord decreases gradually to zero. The results reveal that the quantum entanglement and classical correlation are lost, but the quantum discord continues to reflect quantum information in the same evolving period. For a larger photon number, the oscillations disappear. It is surprised that there exists a transition of quantum discord between classical loss and quantum increasing of correlations for a purely dephasing mode. For a larger photon number in the Y-state, the transition disappears. Moreover, we show that the environment-dependent models can delay the loss of quantum discord. The results depend strongly on the initial angle, which provide a clue to control the quantum gate of superconducting circuit.