  Entanglement measures find frequent application in the study of topologically
ordered systems, where the presence of topological order is reflected in an
additional contribution to the entanglement of the system. Obtaining this
topological entropy from analytical calculations or numerical simulations is
generally difficult due to the fact that it is an order one correction to
leading terms that scale with the size of the system. In order to distil the
topological entropy, one resorts to extrapolation as a function of system size,
or to clever subtraction schemes that allow to cancel out the leading terms.
Both approaches have the disadvantage of requiring multiple (accurate)
calculations of the entanglement of the system. Here we propose a modification
of conventional entanglement calculations that allows to obtain the topological
entropy of a system from a single measurement of entanglement. In our approach,
we replace the conventional trace over the degrees of freedom of a partition of
the system with a projection onto a given state (which needs not be known). We
show that a proper choice of partition and projective measurement allows to rid
the entanglement measures of the typical boundary terms, thus exposing the
topological contribution alone. We consider specifically the measures known as
von Neumann entropy and entanglement negativity, and we discuss their
application to both models that exhibit quantum as well as classical
topological order.
