Exploring the relation between qubit count in entangled systems and the CKW inequality

In this research, we examine the entanglement within two entangled n-qubit systems using the $\pi$-tangle, the sum of the negativities of subsystems, and the sum of the squares of one-tangles. Our findings reveal that in certain states, such as the generalized W state, where probability coefficients depend on the number of qubits, an increase in the number of particles causes the $\pi$-tangle to approach zero, while the CKW inequality converges to equality. In such cases, assessing the system's entanglement can be effectively achieved by summing the negativities of bipartitions or summing the squares of one-tangles. Conversely, in entangled states with probability coefficients independent of the number of qubits, such as the GHZ state, the $\pi$-tangle serves as an appropriate measure for studying the system's entanglement.