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, generalize this strategy to the family of $3 \times n$ magic rectangle games, and supplement these nonlocal games with extra check rounds (of single and pairs of observables).
翻译:自我测试是一种方法来验证一个人从纯古典统计中具有特定量值状态。 对于实际应用, 如设备独立授权的可核实量计算等, 一个自我测试多个贝尔状态并同时将一方所需的量子能力保持在最低水平至关重要 。 在这项工作中, 我们使用 3\ time n$ 魔术矩形游戏( 魔术广场游戏的常规化) 来获取对美方只需测量单方位 Pauli 观测量值的贝尔状态的自我测试 。 协议要求小投入大小( 爱丽丝 和 美元( log n) 元( 鲍勃 ), 并且以坚固的 $O ( n\\ 5/2 }\ qrt \ sqrt\ varepslon} $, 美元是理想( perfect) 关联性( perfect) 与所观察到的相近。 为了实现预期的自我测试, 我们为魔术广场游戏引入一个单方位量子战略, 肯定地取胜, 将这一策略概括为3\ rimember n_ licalbalbalball 和不固定的游戏。