It is one of the peculiar features of quantum physics that some sets of measurements are incompatible in the sense that they cannot be performed simultaneously. Incompatibility is an important quantum resource as it enables Bell nonlocality and steering. Here we show that incompatibility is crucial also in certain communication tasks; we prove that quantum random access code performs better than its classical counterpart only when incompatible quantum measurements are used in the decoding task. As a consequence, evaluating the average success probability for quantum random access code provides a semi-device-independent test for the detection of quantum incompatibility. We further demonstrate that any incompatible pair of projective measurements gives an advantage over all classical strategies. Finally, we establish a connection between the maximal average success probability for quantum random access code and earlier quantities introduced to assess incompatibility.

中文翻译：

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量子随机访问码和测量不兼容

量子物理学的独特特征之一是，某些测量集无法同时执行，因此不兼容。不相容性是重要的量子资源，因为它使Bell具有非局部性和操纵性。在这里，我们表明不兼容在某些沟通任务中也至关重要。我们证明，只有在解码任务中使用了不兼容的量子测量时，量子随机访问代码才能比传统的随机代码具有更好的性能。结果，评估量子随机访问码的平均成功概率为检测量子不兼容性提供了一个与半设备无关的测试。我们进一步证明，任何不兼容的投影测量对都比所有经典策略都具有优势。最后，