  We present a new technique for computing entanglement harvesting with
Unruh-DeWitt particle detectors. The method is particularly useful in cases
where analytic solutions are rare and the Wightman function is known only via
its mode expansion for which numerical integration can become very expensive.
By exploiting the conjugate symmetry of the Wightman function, we may split the
integral into parts dependent on the commutator and anti-commutator of the
field. In cases where the commutator vanishes, such as spacelike separation, or
timelike separation if the strong Huygens principle holds, we then show that
the entangling term of the bipartite density matrix can be expressed in terms
of the much simpler mutual information term. For the vacuum state, this can be
translated into a simple Fourier transform, and thus a single sum over modes,
simplifying the procurement of closed expressions. We demonstrate this for
Minkowski space, finding an analytical solution where none was previously
known.
