论文标题
倾斜的Hardy悖论，用于独立于设备的随机性提取
Tilted Hardy paradoxes for device-independent randomness extraction
论文作者
论文摘要
独立于设备的范式在随机性生成，关键分布和自我测试方面取得了惊人的成功，但是这些结果大多是在当事方拥有可信赖和私人随机种子的假设下获得的。为了放松测量独立性的假设，Hardy的非局部性测试已被提议为理想的候选人。在本文中，我们介绍了一个倾斜的强硬悖论家庭，这些悖论允许自我测试一般的纯纯正两Q Q纠缠状态，并证明多达$ 1 $的本地随机性。然后，我们使用这些倾斜的硬质测试来提高Santha-vazirani（SV）源的最先进的随机性放大协议，并任意有限的测量独立性。我们的结果表明，与任意偏置的SV源和几乎可分离的状态有关设备无关的随机性扩增。最后，我们引入了一个Hardy测试家庭，以最大程度地纠缠的本地尺寸$ 4，8 $作为DI随机性提取的潜在候选者，以证明最高可能的$ 2 \ log d $ d $ d $全球随机性位。
The device-independent paradigm has had spectacular successes in randomness generation, key distribution and self-testing, however most of these results have been obtained under the assumption that parties hold trusted and private random seeds. In efforts to relax the assumption of measurement independence, Hardy's non-locality tests have been proposed as ideal candidates. In this paper, we introduce a family of tilted Hardy paradoxes that allow to self-test general pure two-qubit entangled states, as well as certify up to $1$ bit of local randomness. We then use these tilted Hardy tests to obtain an improvement in the generation rate in the state-of-the-art randomness amplification protocols for Santha-Vazirani (SV) sources with arbitrarily limited measurement independence. Our result shows that device-independent randomness amplification is possible for arbitrarily biased SV sources and from almost separable states. Finally, we introduce a family of Hardy tests for maximally entangled states of local dimension $4, 8$ as the potential candidates for DI randomness extraction to certify up to the maximum possible $2 \log d$ bits of global randomness.
