Quantum correlations of two qubits indefinitely interacting with dephasing environments

Quantum correlations are studied for a two-qubit system which indefinitely interacts with its environments via dephasing coupling, where the indefiniteness is created by a control qubit. The time evolution of the whole system is assumed to be modeled in terms of an exactly solvable spin-boson model. The reduced dynamics of the two-qubit system is conditioned on an outcome of measurement which is performed on the controlled qubit. The characteristic feature of the conditional dynamics is that diagonal elements of a density matrix change in time due to the environmental indefiniteness, in spite of the pure dephasing process. Entanglement, non-local correlation and quantum discord of the two qubits as well as their coherence and energy are examined.