Popescu-Rohrlich correlations imply efficient instantaneous nonlocal quantum computation

TL;DR

This paper demonstrates that nonlocal correlations modeled by Popescu-Rohrlich boxes enable efficient instantaneous nonlocal quantum computation with only linear entanglement, challenging previous assumptions about communication requirements.

Contribution

It shows that nonlocal correlations reduce entanglement needs for quantum computation, establishing a quantum analogue of classical communication complexity collapse.

Findings

Linear entanglement suffices for nonlocal quantum computation with PR-box correlations

Secure position-based cryptography is impossible against non-signalling adversaries

Establishes a quantum analogue of classical communication complexity collapse

Abstract

In instantaneous nonlocal quantum computation, two parties cooperate in order to perform a quantum computation on their joint inputs, while being restricted to a single round of simultaneous communication. Previous results showed that instantaneous nonlocal quantum computation is possible, at the cost of an exponential amount of prior shared entanglement (in the size of the input). Here, we show that a linear amount of entanglement suffices, (in the size of the computation), as long as the parties share nonlocal correlations as given by the Popescu-Rohlich box. This means that communication is not required for efficient instantaneous nonlocal quantum computation. Exploiting the well-known relation to position-based cryptography, our result also implies the impossibility of secure position-based cryptography against adversaries with non-signalling correlations. Furthermore, our construction establishes a quantum analogue of the classical communication complexity collapse under non-signalling correlations.