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(logn) bits for Bob) and is robust with robustness
O(n5/2ε), 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).Comment: 29 pages, 6 figures; v3 minor corrections and changes in response to
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