  We show how the choice of an inflationary state that entangles scalar and
tensor fluctuations affects the angular two-point correlation functions of the
$T$, $E$, and $B$ modes of the cosmic microwave background. The propagators for
a state starting with some general quadratic entanglement are solved exactly,
leading to predictions for the primordial scalar-scalar, tensor-tensor, and
scalar-tensor power spectra. These power spectra are expressed in terms of
general functions that describe the entangling structure of the initial state
relative to the standard Bunch-Davies vacuum. We illustrate how such a state
would modify the angular correlations in the CMB with a simple example where
the initial state is a small perturbation away from the Bunch-Davies state.
Because the state breaks some of the rotational symmetries, the angular power
spectra no longer need be strictly diagonal.
