Entanglement monogamy in a three-qubit state
Jie-Hui Huang, Shi-Yao Zhu · Physical Review A · 2008
We investigate the monogamy nature of entanglement in a three-qubit system. A monogamy inequality is presented to describe the exclusive relation between the $A\text{\ensuremath{-}}B$ two-qubit concurrence ${C}_{AB}$ and the $AB\text{\ensuremath{-}}C$ three-qubit concurrence ${C}_{(AB)C}$, 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 $\mathit{C}$ $({C}_{AC})$ and the concurrence between qubits $\mathit{B}$ and $\mathit{C}$ $({C}_{BC})$ are both given or one of the two is provided.