We investigate how much randomness can be extracted from a generic partially entangled pure state of two qubits in a device-independent setting, where a Bell test is used to certify the correct functioning of the apparatus. For any such state, we first show that two bits of randomness are always attainable both if projective measurements are used to generate the randomness globally or if a nonprojective measurement is used to generate the randomness locally. We then prove that the maximum amount of randomness that can be generated using nonprojective measurements globally is restricted to between approximately 3.58 and 3.96 bits. The upper limit rules out that a bound of four bits potentially obtainable with extremal qubit measurements can be attained. We point out this is a consequence of the fact that nonprojective qubit measurements with four outcomes can only be self-tested to a limited degree in a Bell experiment.

中文翻译：

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部分纠缠态的最大随机性

我们研究了在与设备无关的设置中，从两个量子位的一般部分纠缠的纯态中可以提取多少随机性，其中使用Bell测试来证明设备的正确功能。对于任何这样的状态，我们首先表明，无论是使用投影度量整体生成随机性还是使用非投影度量局部生成随机性，都总是可以获得两个随机性。然后，我们证明使用全局非投影测量可以生成的最大随机量被限制在大约3.58和3.96位之间。上限排除了可以通过极值量子位测量获得的四个位的边界。