Self-testing is a powerful certification of quantum systems relying on measured, classical statistics. This paper considers self-testing in bipartite Bell scenarios with small number of inputs and outputs, but with quantum states and measurements of arbitrarily large dimension. The contributions are twofold. Firstly, it is shown that every maximally entangled state can be self-tested with four binary measurements per party. This result extends the earlier work of Mančinska-Prakash-Schafhauser (2021), which applies to maximally entangled states of odd dimensions only. Secondly, it is shown that every single binary projective measurement can be self-tested with five binary measurements per party. A similar statement holds for self-testing of projective measurements with more than two outputs. These results are enabled by the representation theory of quadruples of projections that add to a scalar multiple of the identity. Structure of irreducible representations, analysis of their spectral features and post-hoc self-testing are the primary methods for constructing the new self-tests with small number of inputs and outputs.

中文翻译：

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最大纠缠态和单投影测量的恒定大小自测试

自测试是对量子系统的一种强有力的认证，它依赖于可测量的经典统计数据。本文考虑在具有少量输入和输出但具有任意大维度的量子态和测量的二分贝尔场景中进行自测试。贡献是双重的。首先，它表明每个最大纠缠态都可以通过每方四个二进制测量进行自测试。这一结果扩展了 Mančinska-Prakash-Schafhauser (2021) 的早期工作，该工作仅适用于奇数维的最大纠缠态。其次，它表明每个单独的二进制投影测量都可以通过每方五个二进制测量进行自测试。类似的说法也适用于具有两个以上输出的投影测量的自测试。这些结果是通过添加到恒等标量倍数的四元投影表示理论实现的。不可约表示的结构、频谱特征分析和事后自测试是构建具有少量输入和输出的新自测试的主要方法。