= Two-qubit Werner state
{title2=$\rho_p=pP_s+(1-p)(I-P_s)/3$}
This collective-unitary-invariant two-qubit state has singlet weight $p$ and equal weights on the three triplet <Bell states>. With $P_s$ the <spin singlet state> projector, its <partial transpose> has eigenvalues $(1-2p)/2$ once and $(1+2p)/6$ three times. It is entangled exactly when $p>1/2$. At $p=1/2$, it is the equally weighted mixture of six antiparallel product states along the three Pauli axes. In the interval $1/4\leq p\leq1/2$, convex mixing of this boundary state with $I/4$ explicitly proves separability. The weight $p$ here is the singlet probability, not the alternative coefficient multiplying a pure singlet in a white-noise mixture.
Back to article page
