Robust self-testing of many-qubit states

TL;DR

This paper presents a simple, robust two-player test that certifies the correct application of tensor products of Pauli observables on multiple EPR pairs, with applications in quantum verification and computation.

Contribution

It introduces the first robust self-test for many EPR pairs and develops applications in quantum proof systems and delegated quantum computation.

Findings

Achieves constant robustness in self-testing of many-qubit states.

Provides a quantum multiprover proof system with size-independent gap.

Develops a robust protocol for delegated quantum computation.

Abstract

We introduce a simple two-player test which certifies that the players apply tensor products of Pauli $\sigma_X$ and $\sigma_Z$ observables on the tensor product of $n$ EPR pairs. The test has constant robustness: any strategy achieving success probability within an additive $\varepsilon$ of the optimal must be $\mathrm{poly}(\varepsilon)$-close, in the appropriate distance measure, to the honest $n$-qubit strategy. The test involves $2n$-bit questions and $2$-bit answers. The key technical ingredient is a quantum version of the classical linearity test of Blum, Luby, and Rubinfeld. As applications of our result we give (i) the first robust self-test for $n$ EPR pairs; (ii) a quantum multiprover interactive proof system for the local Hamiltonian problem with a constant number of provers and classical questions and answers, and a constant completeness-soundness gap independent of system size; (iii) a robust protocol for delegated quantum computation.