  We define a notion of target space entanglement entropy. Rather than
partitioning the base space on which the theory is defined, we consider
partitions of the target space. This is the physical case of interest for
first-quantized theories, such as worldsheet string theory. We associate to
each subregion of the target space a suitably chosen sub-algebra of observables
$\mathcal{A}$. The entanglement entropy is calculated as the entropy of the
density matrix restricted to $\mathcal{A}$. As an example, we illustrate our
framework by computing spatial entanglement in first-quantized many-body
quantum mechanics. The algebra $\mathcal{A}$ is chosen to reproduce the
entanglement entropy obtained by embedding the state in the fixed particle
sub-sector of the second-quantized Hilbert space. We then generalize our
construction to the quantum field-theoretical setting.
