In device-independent (DI) quantum protocols, the security statements are oblivious to the characterization of the quantum apparatus - they are based solely on the classical interaction with the quantum devices as well as some well-defined assumptions. The most commonly known setup is the so-called non-local one, in which two devices that cannot communicate between themselves present a violation of a Bell inequality. In recent years, a new variant of DI protocols, that requires only a single device, arose. In this novel research avenue, the no-communication assumption is replaced with a computational assumption, namely, that the device cannot solve certain post-quantum cryptographic tasks. The protocols for, e.g., randomness certification, in this setting that have been analyzed in the literature used ad hoc proof techniques and the strength of the achieved results is hard to judge and compare due to their complexity. Here, we build on ideas coming from the study of non-local DI protocols and develop a modular proof technique for the single-device computational setting. We present a flexible framework for proving the security of such protocols by utilizing a combination of tools from quantum information theory, such as the entropic uncertainty relation and the entropy accumulation theorem. This leads to an insightful and simple proof of security, as well as to explicit quantitative bounds. Our work acts as the basis for the analysis of future protocols for DI randomness generation, expansion, amplification and key distribution based on post-quantum cryptographic assumptions.

翻译：在设备无关（DI）量子协议中，安全声明与量子设备的表征无关——它们完全基于与量子设备的经典交互以及一些明确定义的假设。最常见的设置是所谓的非局域设置，其中两个无法相互通信的设备呈现贝尔不等式的违反。近年来，出现了一种仅需单个设备的新型DI协议变体。在这条新兴研究路径中，无通信假设被替换为计算假设，即设备无法解决某些后量子密码学任务。该设置下用于随机性认证等目标的协议，在文献中使用特设证明技术进行分析，且因复杂度较高，其结果的有效性难以评判与比较。本文借鉴非局域DI协议研究中的思想，为单设备计算设置开发了一种模块化证明技术。通过利用量子信息论中的工具组合（例如熵不确定关系与熵累积定理），我们提出了一个灵活的框架来证明此类协议的安全性。这带来了深刻且简单的安全证明，并给出了明确的定量界限。我们的工作为基于后量子密码学假设的DI随机数生成、扩展、放大及密钥分发等未来协议分析奠定了基础。