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

TL;DR

This paper introduces new protocols for instantaneous non-local quantum measurements and multipartite quantum computation that significantly reduce entanglement use, impacting the security of position-based cryptography.

Contribution

It presents protocols that lower entanglement consumption exponentially and establishes bounds on entanglement needed for non-local measurements, advancing quantum cryptography techniques.

Findings

Protocols reduce entanglement consumption exponentially.

A linear lower bound on entanglement for non-local measurements is proven.

Exponential entanglement scaling compromises position-based cryptography security.

Abstract

Instantaneous measurements of non-local observables between space-like separated regions can be performed without violating causality. This feat relies on the use of entanglement. Here we propose novel protocols for this task and the related problem of multipartite quantum computation with local operations and a single round of classical communication. Compared to previously known techniques, our protocols reduce the entanglement consumption by an exponential amount. We also prove a linear lower bound on the amount of entanglement required for the implementation of a certain non-local measurement. These results relate to position-based cryptography: an amount of entanglement scaling exponentially in the number of communicated qubits is sufficient to render any such scheme insecure. Furthermore, we show that certain schemes are secure under the assumption that the adversary has less entanglement than a given linear bound and is restricted to classical communication.