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Instantaneous measurements of non-local observables between space-likeseparated regions can be performed without violating causality. This featrelies on the use of entanglement. Here we propose novel protocols for thistask and the related problem of multipartite quantum computation with localoperations and a single round of classical communication. Compared topreviously known techniques, our protocols reduce the entanglement consumptionby an exponential amount. We also prove a linear lower bound on the amount ofentanglement required for the implementation of a certain non-localmeasurement.  These results relate to position-based cryptography: an amount ofentanglement scaling exponentially in the number of communicated qubits issufficient to render any such scheme insecure. Furthermore, we show thatcertain schemes are secure under the assumption that the adversary has lessentanglement than a given linear bound and is restricted to classicalcommunication.

Simplified instantaneous non-local quantum computation with applications to position-based cryptography