Consider a system composed of two subsystems $A$ and $B$ living in $\mathcal{H}=\mathcal{H}_A \otimes \mathcal{H}_B$. The density matrix of the system $AB$ is defined to be $\rho$. The entanglement negativity of $\rho^{T_A}$, $\mathcal{N}(\rho^{T_A})$, measures by how much $\rho^{T_A}$ fails to be positive semidefinite. This is useful since would $AB$ be separable, $\rho^{T_A}$ would be positive semidefinite, hence unentangled ($\mathcal{N}=0$). This, along with some other nice properties makes $\mathcal{N}$ a nice entanglement measure. 

What I don’t understand is why one can **specifically** interpret $\mathcal{N}(\rho^{T_A})$ as the entanglement between $A$ and $B$.

Why is this true?