Time optimal realization of two-qubit entangler

Optimal control theory is a versatile tool applied to decompose unitary quantum operations into a sequence of entangling and single-qubit gates. Here, we seek a systematic way to find time-optimal pulse sequences to transfer coherence in both mixed and pure states and produce an entangling gate in quantum networks. To this end, we use the algebra of Dirac γ matrices to reduce the problem to actual variables and, by applying a Cartan decomposition to SO (4), we formulate the optimal control problem and give an operational approach to realize the entangler gate experimentally. We produce an arbitrary perfect two-qubit entangler, creating a maximally-entangled state out of some initial product state. Also, we calculate the geometric discord and the optimal time required to steer an initial state with zero discord into a mixed state with maximum discord in two-qubit systems.