# How to check if a two-qubit gate is entangling?

I would like to know if there's an analog for Schmidt rank that can tell me if a two-qubit unitary is entangling?

Suppose I have a parametrized two-qubit unitary $$U^{(2)}(\theta)$$. I would like to know a test to tell the degree of entanglement this gate produces, ideally as a function of $$\theta$$.

For example, given the following matrix:

$$A = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & e^{i\theta} & 0 \\ 0 & 0 & 0 & -e^{i\theta} \\ \end{pmatrix}$$

the test should tell me that that $$A \propto Z \otimes R_z(\theta)$$ is not entangling. But given the matrix: $$B = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & e^{-i\theta} & 0 \\ 0 & 0 & 0 & e^{i\theta} \\ \end{pmatrix}$$ the test should tell me that $$B = CR_z(\theta)$$ is entangling (provided $$\theta \neq 0$$). In the best case, the test would yield some degree of entanglement as a function of $$\theta$$ though such a metric may depend on the initial state instead of just the gate...