We investigate the monogamy nature of entanglement in a three-qubit system. A monogamy inequality is presented to describe the exclusive relation between the $A\text{−}B$ two-qubit concurrence $C_{AB}$ and the $AB\text{−}C$ three-qubit concurrence $C_{\left(AB\right)C}$, which represents the entanglement between qubits $\mathit{A}$ and $\mathit{B}$ as a whole and the third qubit $\mathit{C}$. It is found that the entanglement between any two qubits in a three-qubit system is limited by the entanglement between these two qubits and another qubit. As a consequence, we present the upper bounds for the concurrence $C_{AB}$, when the concurrence between qubits $\mathit{A}$ and $\mathit{C}$ $\left(C_{AC}\right)$ and the concurrence between qubits $\mathit{B}$ and $\mathit{C}$ $\left(C_{BC}\right)$ are both given or one of the two is provided.

• Received 3 May 2008

DOI:https://doi.org/10.1103/PhysRevA.78.012325