Matilde Baroni - Quantum bounds for compiled XOR games and d-outcome CHSH games

Quantum bounds for compiled XOR games and d-outcome CHSH games

This seminar, given by Matilde Baroni, will happend on 15 May 2024, at 9:45. It will take place in Room Not specified.

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Abstract

Nonlocal games play a crucial role in quantum information theory and have numerous applications in certification and cryptographic protocols. Kalai et al. (STOC 2023) introduced a procedure to compile a nonlocal game into a single-prover interactive proof, using a quantum homomorphic encryption scheme, and showed that their compilation method preserves the classical bound of the game. Natarajan and Zhang (FOCS 2023) then showed that the quantum bound is preserved for the specific case of the CHSH game. Extending the proof techniques of Natarajan and Zhang, we show that the compilation procedure of Kalai et al. preserves the quantum bound for two classes of games: XOR games and d-outcome CHSH games. We also establish that, for any pair of qubit measurements, there exists a compiled XOR game such that its near-optimal winning probability serves as a robust self-test for that particular pair of measurements. Finally, we derive computational self-testing of three anticommuting qubit observables, based on the compilation of the nonlocal game corresponding to the so-called elegant Bell inequality.