Practical parallel self-testing of Bell states via magic rectangles
This work addresses a practical need for device-independent delegated verifiable quantum computation, representing an incremental improvement in parallel self-testing methods.
The authors tackled the problem of verifying multiple Bell states in parallel with minimal quantum requirements, achieving a self-test for n Bell states using single-qubit Pauli measurements with small input sizes and robustness scaling as O(n^{5/2} √ε).
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 $3 \times n$ 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 $O(n^{5/2} \sqrt{\varepsilon})$, where $\varepsilon$ 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, we generalize this strategy to the family of $3 \times n$ magic rectangle games, and we supplement these nonlocal games with extra check rounds (of single and pairs of observables).