Robust self-testing of many-qubit states

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 $\epsilon$ of the optimal must be $\mathrm{poly}(\epsilon )$-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.

36 pages. Improves upon and supersedes our earlier submission arXiv:1512.02090

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• Robust Self Testing of the Singlet
• Robust self-testing of many-qubit states
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