Swap operator ($F$)

The swap operator exchanges two tensor factors: $F(|\psi ⟩\otimes |\varphi ⟩)=|\varphi ⟩\otimes |\psi ⟩$. It has eigenvalue $+1$ on the symmetric subspace and $-1$ on the antisymmetric subspace, and the partial transpose of $|{\Phi }^{+}⟩⟨{\Phi }^{+}|$ is $F/d$.