The paper by Valerie Coffman, Joydip Kundu, and William K. Wootters explores the relationship between entanglement among three qubits A, B, and C. They introduce the concept of the "tangle," a measure of entanglement related to the entanglement of formation, to quantify the trade-off between A's entanglement with B and its entanglement with C. Specifically, they show that the tangle between A and B plus the tangle between A and C cannot exceed the tangle between A and the pair BC. This inequality is optimal, meaning that for any values of the tangles satisfying the equality, there exists a quantum state consistent with those values. The authors further define a "three-way tangle" that measures the entanglement of the system as a whole and is invariant under permutations of the qubits. They provide a detailed derivation of these results and discuss their implications, including the connection to other measures of entanglement and the behavior of mixed states. The paper also highlights the significance of these findings in the broader context of quantum information theory and entanglement manipulation.The paper by Valerie Coffman, Joydip Kundu, and William K. Wootters explores the relationship between entanglement among three qubits A, B, and C. They introduce the concept of the "tangle," a measure of entanglement related to the entanglement of formation, to quantify the trade-off between A's entanglement with B and its entanglement with C. Specifically, they show that the tangle between A and B plus the tangle between A and C cannot exceed the tangle between A and the pair BC. This inequality is optimal, meaning that for any values of the tangles satisfying the equality, there exists a quantum state consistent with those values. The authors further define a "three-way tangle" that measures the entanglement of the system as a whole and is invariant under permutations of the qubits. They provide a detailed derivation of these results and discuss their implications, including the connection to other measures of entanglement and the behavior of mixed states. The paper also highlights the significance of these findings in the broader context of quantum information theory and entanglement manipulation.