Practical Parallel Self-testing of Bell States via Magic Rectangles
Practical Parallel Self-testing of Bell States via Magic Rectangles
复制标题
DOI：
10.1103/physreva.105.032456
复制
发表时间：
2021-05
期刊：
影响因子：
--
通讯作者：
Sean A. Adamson;P. Wallden
中科院分区：
文献类型：
--
作者：
Sean A. Adamson;P. Wallden
自测试是一种从纯粹的经典统计中验证一个人具有特定量子态的方法。对于实际应用，例如独立于设备的委托可验证量子计算，至关重要的是并行自测多个Bell状态，同时保持一侧所需的量子能力最小化。在这项工作中，我们使用$3 \times n$魔术矩形游戏（幻方游戏的推广），以获得一个自我测试的$n$贝尔状态，其中一方只需要测量单量子比特泡利观测。该协议需要较小的输入大小[Alice为常数，Bob为$O（\log n）$ bits]，并且具有鲁棒性$O（n^{5/2} \sqrt{\vareps}）$，其中$\vareps $是理想（完美）相关性与观察到的相关性的接近程度。为了实现所需的自我测试，我们引入了一个单边局部量子策略的幻方游戏，赢得了确定性，我们将此策略推广到家庭的3\times n$幻方游戏，我们补充这些非局部游戏与额外的检查轮（单个和对的可观测量）。
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).