= Isotropic quantum state
= Isotropic state
{synonym}
For two $d$-dimensional systems, an isotropic quantum state has the form
$$
\rho_p=p|\Phi^+\rangle\langle\Phi^+|+(1-p)\frac{I}{d^2},
$$
where $|\Phi^+\rangle=d^{-1/2}\sum_j|jj\rangle$ is a <maximally entangled state>. This parametrization is separable exactly when $p\leq1/(d+1)$.
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.
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