AI 中文总结
该研究将Navascués-Pironio-Acín层级适配能量受限场景，构造半定规划松弛，证明即使存在全量子敌手，能量受限的半设备无关框架中仍可实现认证随机性生成。
AI 中文摘要
基于能量约束的制备-测量框架在全设备依赖和设备无关量子密码学之间提供了实用的中间方案。该框架对原本未表征的制备-测量设备仅做一个假设：制备态的能量是有界的。现有对该框架的安全性分析假设制备和测量设备最多共享经典关联，在该假设下已建立了可提取随机性的认证下界。近期研究表明，若敌手在设备间预分配纠缠，其攻击能力将远强于设备仅共享经典关联时的攻击，会将可提取随机性降至低于之前认证的速率。这留下了一个基本问题：在该场景中是否根本无法认证随机性？我们通过将Navascués-Pironio-Acín层级适配至允许设备间共享纠缠的能量受限场景，构造了猜测概率的半定规划松弛。我们的松弛方法在不对制备和测量设备间共享的量子态维度施加任何限制的情况下，得到了可提取随机性的认证下界。我们证明，在一系列能量值下，这些认证下界严格为正，从而肯定地回答了该开放问题：即使存在全量子敌手，在能量受限的半设备无关（SDI）框架中，理论上仍可实现认证随机性生成。
英文摘要
The prepare-and-measure framework based on energy constraints offers a practical middle ground between fully device-dependent and device-independent quantum cryptography. The only assumption on an otherwise uncharacterized prepare-and-measure device is that the energy of the prepared states is bounded. Existing security analyses of this framework assume that the preparation and measurement devices share at most classical correlations, and under this assumption certified lower bounds on the extractable randomness have been established. Recent work has shown that an adversary who pre-distributes entanglement between the devices can mount attacks that are strictly more powerful than those available when the devices share only classical correlations, reducing the extractable randomness below the previously certified rates. This leaves open the fundamental question of whether randomness can be certified at all in this scenario. We address this open question by constructing semidefinite programming relaxations of the guessing probability by adapting the Navascués-Pironio-Acín hierarchy to the energy-constrained setting where shared entanglement between the devices is permitted. Our relaxations yield certified lower bounds on the extractable randomness without enforcing any restrictions on the dimensions of the quantum state shared between the preparation and measurement devices. We show that these certified lower bounds are strictly positive for a range of energy values, thereby answering the open question affirmatively: certified randomness generation is theoretically possible in the energy-constrained SDI framework even in the presence of a fully quantum adversary.
Comments6 + 6 pages, 5 figures
