Practical parallel self-testing of Bell states via magic rectangles

Self-testing is a method to verify that one has a particular quantum state from purely classical statistics. For practical applications, such as device-independent delegated verifiable quantum computation, it is crucial that one self-tests multiple Bell states in parallel while keeping the quantum capabilities required of one side to a minimum. In this work, we use the 3 × n magic rectangle games (generalizations of the magic square game) to obtain a self-test for n Bell states where the one side needs only to measure single-qubit Pauli observables. The protocol requires small input sizes (constant for Alice and O(log n) bits for Bob) and is robust with robustness O(n 5/2√ ε), where ε is the closeness of the ideal (perfect) correlations to those observed. To achieve the desired self-test we introduce a one-side-local quantum strategy for the magic square game that wins with certainty, generalize this strategy to the family of 3×n magic rectangle games, and supplement these nonlocal games with extra check rounds (of single and pairs of observables).