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In a bipartite system $AB$, why does the entanglement negativity $\mathcal{N}(\rho^{T_A})$ measure the entanglement between $A$ and $B$?

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?