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Self-testing is a method to verify that one has a particular quantum statefrom purely classical statistics. For practical applications, such asdevice-independent delegated verifiable quantum computation, it is crucial thatone self-tests multiple Bell states in parallel while keeping the quantumcapabilities required of one side to a minimum. In this work, we use the $3\times n$ magic rectangle games (generalizations of the magic square game) toobtain a self-test for $n$ Bell states where the one side needs only to measuresingle-qubit Pauli observables. The protocol requires small input sizes[constant for Alice and $O(\log n)$ bits for Bob] and is robust with robustness$O(n^{5/2} \sqrt{\varepsilon})$, where $\varepsilon$ is the closeness of theideal (perfect) correlations to those observed. To achieve the desiredself-test, we introduce a one-side-local quantum strategy for the magic squaregame that wins with certainty, we generalize this strategy to the family of $3\times n$ magic rectangle games, and we supplement these nonlocal games withextra check rounds (of single and pairs of observables).

Practical parallel self-testing of Bell states via magic rectangles