Isotropic quantum state

For two $d$-dimensional systems, an isotropic quantum state has the formwhere $|{\Phi }^{+}⟩=d^{-1/2}{\sum }_j|jj⟩$ is a maximally entangled state. This parametrization is separable exactly when $p\le 1/(d+1)$.

The defining symmetry is $U\otimes \overline{U}$ invariance. This differs from the $U\otimes U$ invariance of a Werner state; members above the displayed threshold are entangled.