Entanglement-changing power of two-qubit unitary operations

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Entanglement-changing power of an arbitrary two-qubit operation, including increasing and decreasing power, is investigated in this paper. We consider the maximal entanglement ${C}_{\mathrm{max}}$ and the minimal entanglement ${C}_{\mathrm{min}}$ of the states obtained by a given two-qubit unitary operation ${U}_{d}$ acting on arbitrary pure states with fixed entanglement ${C}_{0}$. We give the condition that the maximal entanglement ${C}_{\mathrm{max}}$ of the obtained states can be $1$ and the minimal entanglement ${C}_{\mathrm{min}}$ can be $0$. When the maximal entanglement ${C}_{\mathrm{max}}$ cannot be $1$, we give the maximal value it can reach. When the minimal entanglement ${C}_{\mathrm{min}}$ cannot be $0$, we give the minimal value it can reach. We think ${C}_{\mathrm{max}}$ and ${C}_{\mathrm{min}}$ represent the entanglement-changing power of two-qubit unitary operations.