无界维状态和测量的常数鲁棒自检验
Constant-sized robust self-tests for states and measurements of unbounded dimension
摘要：
我们考虑相关性，$p_{n,x}$，产生于测量一个最大的纠缠态使用$n$测量两个结果，从$n$的预测，加起来$xI$。我们表明，相关性$p_{n,x}$强大的自我测试的基础状态和测量。为了实现这一点，我们解除了基于群理论的Gowers-Hatami方法，用于证明更自然的代数框架的强大的自我测试。一个关键步骤是获得一个类似的Gowers-Hatami定理允许扰动的“近似”表示的相关代数的一个确切的。对于$n=4$，关联$p_{n,x}$自检验每个奇数维的最大纠缠态以及任意高秩的2-结果投影测量。唯一的另一个家族的常数大小的自测试的无限维的战略是由于傅（QIP 2020）谁提出了这样的自测试的无限家族的最大纠缠态甚至本地维。因此，我们是第一个展示了一个常数大小的自我测试的测量无界尺寸以及所有的最大纠缠态与奇的局部尺寸。
英文摘要：
We consider correlations, $p_{n,x}$, arising from measuring a maximally entangled state using $n$ measurements with two outcomes each, constructed from $n$ projections that add up to $xI$. We show that the correlations $p_{n,x}$ robustly self-test the underlying states and measurements. To achieve this, we lift the group-theoretic Gowers-Hatami based approach for proving robust self-tests to a more natural algebraic framework. A key step is to obtain an analogue of the Gowers-Hatami theorem allowing to perturb an "approximate" representation of the relevant algebra to an exact one. For $n=4$, the correlations $p_{n,x}$ self-test the maximally entangled state of every odd dimension as well as 2-outcome projective measurements of arbitrarily high rank. The only other family of constant-sized self-tests for strategies of unbounded dimension is due to Fu (QIP 2020) who presents such self-tests for an infinite family of maximally entangled states with even local dimension. Therefore, we are the first to exhibit a constant-sized self-test for measurements of unbounded dimension as well as all maximally entangled states with odd local dimension.
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