  We present three families of exact, cohomogeneity-one Einstein metrics in
$(2n+2)$ dimensions, which are generalizations of the Stenzel construction of
Ricci-flat metrics to those with a positive cosmological constant. The first
family of solutions are Fubini-Study metrics on the complex projective spaces
$CP^{n+1}$, written in a Stenzel form, whose principal orbits are the Stiefel
manifolds $V_2(R ^{n+2})=SO(n+2)/SO(n)$ divided by $Z_2$. The second family are
also Einstein-K\"ahler metrics, now on the Grassmannian manifolds
$G_2(R^{n+3})=SO(n+3)/((SO(n+1)\times SO(2))$, whose principal orbits are the
Stiefel manifolds $V_2(R^{n+2})$ (with no $Z_2$ factoring in this case). The
third family are Einstein metrics on the product manifolds $S^{n+1}\times
S^{n+1}$, and are K\"ahler only for $n=1$. Some of these metrics are believed
to play a role in studies of consistent string theory compactifications and in
the context of the AdS/CFT correspondence. We also elaborate on the geometric
approach to quantum mechanics based on the K\"ahler geometry of Fubini-Study
metrics on $CP^{n+1}$, and we apply the formalism to study the quantum
entanglement of qubits.
