基于能量约束的对抗量子敌手的认证随机性生成
Certified Randomness Generation against Quantum Adversaries via Energy Constraints
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中文总结 AI 辅助
本研究提出一种基于能量约束的制备-测量QRNG，证明单轮冯·诺依曼熵的紧下界，显著提升认证随机性生成的安全性与速率。
中文摘要 AI 辅助
对于量子随机数生成器（QRNG），在各种假设下可以获得强大的安全保证。最著名的假设是非信号假设（设备无关（DI）QRNG所需）和后量子计算假设（计算受限的单证明者QRNG协议所需）。在这项工作中，我们研究了第三种模型：一个简单的制备-测量QRNG，其安全性依赖于物理动机的能量约束。这种物理动机的设置允许更容易地实现QRNG，并能提供更好的速率。到目前为止，先前研究能量约束模型的工作要么在安全证明中假设敌手是经典的，要么通过限制条件最小熵来提供相对较弱的认证随机性界限。在这项工作中，我们证明了针对同时持有经典和量子侧信息的敌手，单轮冯·诺依曼熵的一个新的、本质上紧的下界。我们的工作揭示了在量子情况下使用冯·诺依曼熵而非最小熵可以带来重大改进，在许多情况下几乎匹配经典界限。我们进一步研究了我们的熵界的鲁棒性。由于单轮冯·诺依曼熵是表征QRNG密钥率的主要量，我们的界为该框架中针对一般量子攻击的严格安全证明建立了主要成分。
英文摘要
For quantum random number generators (QRNGs), strong security guarantees can be obtained under various assumptions. The most well-known assumptions are the non-signalling assumption (needed for device-independent (DI) QRNG) and post-quantum computational assumptions (needed for computationally bounded single-prover QRNG protocols). In this work, we study a third model: a simple prepare-and-measure QRNG whose security relies on physically motivated energy constraints. This physically motivated set-up allows for easier implementations of QRNGs and can supply better rates. So far, previous works that studied the energy-constrained model either assumed that the adversary is classical in their security proof or supplied relatively weak bounds on the certified randomness, by bounding the conditional min-entropy. In this work, we prove a new, essentially tight, lower bound on the single-round von Neumann entropy against adversaries holding both classical and quantum side-information. Our work reveals that working with the von Neumann entropy, rather than the min-entropy, in the quantum case can lead to a major improvement, nearly matching the classical bound in many cases. We further study the robustness of our entropy bound. Since the single-round von Neumann entropy is the main quantity of interest when characterizing the key rate of QRNGs, our bound establishes the main ingredient for rigorous security proofs against general quantum attacks in this framework.
发表机构
- Weizmann Institute of Science（魏茨曼科学研究所）
- École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）
- LMU Munich（慕尼黑大学）
- Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）
机构由 AI 辅助整理，请以论文原文为准。
