Anand Natarajan: Robust self-testing of many qubit states

Опубликовано 1 февраля 2017, 1:29

"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 $\eps$ of the optimal must employ a strategy that is $\poly(\eps)$-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 the first robust self-test for $n$ EPR pairs; a quantum multiprover interactive proof system for the local Hamiltonian problem with a constant number of provers, classical questions and answers, and a constant completeness-soundness gap independent of system size; and a robust protocol for delegated quantum computation."