  We characterize the state space of a Toeplitz-Cuntz algebra TO_n in terms of
positive operator matrices $\Omega$ on Fock space which satisfy sl(\Omega) \le
\Omega, where sl(\Omega) is the operator matrix obtained from \Omega by taking
the trace in the last variable. Essential states correspond to those matrices
\Omega which are slice-invariant. As an application we show that a pure
essential product state of the fixed-point algebra for the action of the gauge
group has precisely a circle of pure extensions to TO_n.
