Bell nonlocality as a resource for device-independent certification schemes has been studied extensively in recent years. The strongest form of device-independent certification is referred to as self-testing, which given a device, certifies the promised quantum state as well as quantum measurements performed on it without any knowledge of the internal workings of the device. In spite of various results on self-testing protocols, it remains a highly nontrivial problem to propose a certification scheme of qudit–qudit entangled states based on violation of a single d-outcome Bell inequality. Here we address this problem and propose a self-testing protocol for the maximally entangled state of any local dimension using the minimum number of measurements possible, i.e., two per subsystem. Our self-testing result can be used to establish unbounded randomness expansion, \({{{\mathrm{log}}}\,}_{2}d\) perfect random bits, while it requires only one random bit to encode the measurement choice.

近年来，贝尔非局域性作为独立于设备的认证计划的资源得到了广泛研究。与设备无关的最强大的认证形式称为自测试，它在给定设备的情况下，在不了解设备内部工作原理的情况下验证承诺的量子状态以及对其执行的量子测量。尽管在自测试协议上有各种结果，但提出基于违反单个d的 qudit-qudit 纠缠状态的认证方案仍然是一个非常重要的问题- 结果贝尔不等式。在这里，我们解决了这个问题，并为任何局部维度的最大纠缠状态提出了一种自测试协议，使用可能的最少测量次数，即每个子系统两个。我们的自测结果可用于建立无界随机扩展，\({{{\mathrm{log}}}\,}_{2}d\)完美随机位，而它只需要一个随机位来编码测量选择。