Title: Quantifying Coherence with Untrusted Devices Show Chinese title

Title: 用不可信设备量化相干性

Abstract: Device-independent (DI) tests allow to witness and quantify the quantum feature of a system, such as entanglement, without trusting the implementation devices. Although DI test is a powerful tool in many quantum information tasks, it generally requires nonlocal settings. Fundamentally, the superposition property of quantum states, quantified by coherence measures, is a distinct feature to distinguish quantum mechanics from classical theories. In literature, witness and quantification of coherence with trusted devices have been well-studied. However, it remains open whether we can witness and quantify single party coherence with untrusted devices, as it is not clear whether the concept of DI tests exists without a nonlocal setting. In this work, we study DI witness and quantification of coherence with untrusted devices. First, we prove a no-go theorem for a fully DI scenario, as well as a semi DI scenario employing a joint measurement with trusted ancillary states. We then propose a general prepare-and-measure semi DI scheme for witnessing and quantifying the amount of coherence. We show how to quantify the relative entropy and the $l_1$ norm of single party coherence with analytical and numerical methods. As coherence is a fundamental resource for tasks such as quantum random number generation and quantum key distribution, we expect our result may shed light on designing new semi DI quantum cryptographic schemes. Show Chinese abstract

Abstract: 设备无关（DI）测试允许在不信任实现设备的情况下，见证和量化系统的量子特性，例如纠缠。 尽管DI测试是许多量子信息任务中的强大工具，但它通常需要非定域设置。 从根本上说，量子态的叠加性质，通过相干性度量来量化，是区分量子力学与经典理论的显著特征。 在文献中，使用可信设备的相干性见证和量化已被深入研究。 然而，是否可以在不可信设备下见证和量化单方相干性仍是一个开放问题，因为不清楚在没有非定域设置的情况下是否存在DI测试的概念。 在本工作中，我们研究了使用不可信设备的DI相干性见证和量化。 首先，我们证明了一个完全DI场景的不可能定理，以及一个采用可信辅助态联合测量的半DI场景。 然后，我们提出了一种通用的准备和测量半DI方案，用于见证和量化相干性的数量。 我们展示了如何用分析和数值方法量化单方相干性的相对熵和$l_1$范数。 由于相干性是量子随机数生成和量子密钥分发等任务的基本资源，我们期望我们的结果可能为设计新的半DI量子密码方案提供启示。