Quantum Advantage from Any Non-local Game

We show a general method of compiling any k-prover non-local game into a single-prover (computationally sound) interactive game maintaining the same quantum completeness and classical soundness guarantees, up to a negligible additive factor in a security parameter. Our compiler uses any quantum homomorphic encryption scheme (Mahadev, FOCS 2018; Brakerski, CRYPTO 2018) satisfying a natural form of correctness with respect to auxiliary quantum input. The homomorphic encryption scheme is used as a cryptographic mechanism to simulate the effect of spatial separation, and is required to evaluate k−1 prover strategies out of k on encrypted queries.