  Relativistic causality has dramatic consequences on the measurability of
nonlocal variables and poses the fundamental question of whether it is
physically meaningful to speak about the value of nonlocal variables at a
particular time. Recent work has shown that by weakening the role of the
measurement in preparing eigenstates of the variable it is in fact possible to
measure all nonlocal observables instantaneously by exploiting entanglement.
However, for these measurement schemes to succeed with certainty an infinite
amount of entanglement must be distributed initially and all this entanglement
is necessarily consumed. In this work we sharpen the characterisation of
instantaneous nonlocal measurements by explicitly devising schemes in which
only a finite amount of the initially distributed entanglement is ever
utilised. This enables us to determine an upper bound to the average
consumption for the most general cases of nonlocal measurements. This includes
the tasks of state verification, where the measurement verifies if the system
is in a given state, and verification measurements of a general set of
eigenstates of an observable. Despite its finiteness the growth of entanglement
consumption is found to display an extremely unfavourable exponential of an
exponential scaling with either the number of qubits needed to contain the
Schmidt rank of the target state or total number of qubits in the system for an
operator measurement. This scaling is seen to be a consequence of the
combination of the generic exponential scaling of unitary decompositions
combined with the highly recursive structure of our scheme required to overcome
the no-signalling constraint of relativistic causality.
