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 has been well-studied. It is an open problem to witness and quantify coherence with untrusted devices. As coherence can arise in a single party quantum state, 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 the existing DI or semi DI means. 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 several 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施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，但它通常需要非局域设置。 根本上，量子态的叠加性质，由相干性度量来量化，是区分量子力学与经典理论的独特特征。 在文献中，使用可信设备来见证和量化相干性已经得到了很好的研究。 使用不可信设备来见证和量化相干性是一个开放问题。 由于相干性可以在单方量子态中出现，不清楚是否存在不需要非局域设置的DI测试概念。 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，我们证明了现有DI或半DI方法的无解定理。 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。 我们展示了如何使用分析和数值方法来量化单方相干性的相对熵和$l_1$范数。 由于相干性是几个任务的基本资源，例如量子随机数生成和量子密钥分发，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。