For certain joint measurements on a pair of spatially separated particles, we
ask how much entanglement is needed to carry out the measurement exactly. For a
class of orthogonal measurements on two qubits with partially entangled
eigenstates, we present upper and lower bounds on the entanglement cost. The
upper bound is based on a recent result by D. Berry [Phys. Rev. A 75, 032349
(2007)]. The lower bound, based on the entanglement production capacity of the
measurement, implies that for almost all measurements in the class we consider,
the entanglement required to perform the measurement is strictly greater than
the average entanglement of its eigenstates. On the other hand, we show that
for any complete measurement in d x d dimensions that is invariant under all
local Pauli operations, the cost of the measurement is exactly equal to the
average entanglement of the states associated with the outcomes.
