打破量子位置验证的有界纠缠壁垒
Breaking the Bounded Entanglement Barrier for Quantum Position Verification
- NTT Research（NTT研究院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出一种基于BB84的量子位置验证协议，在连续时间模型中打破有界纠缠壁垒，实现诚实方资源远小于对手资源，且差距随时间测量精度提升而增大。
AI中文摘要：
位置验证由 Chandran 等人（SIAM J. Computing 2014）提出，允许验证者通过交互协议测试证明者声称的位置。经典位置验证是不可能的。即使在量子位置验证（QPV）中，如果对手能够持有指数级大的预共享纠缠，总是存在 LOCC（局域操作与经典通信）攻击。令人惊讶的是，我们表明在理想化的连续时间模型中，我们可以绕过这一壁垒，其中时间由实值参数表示，挑战消息可以在从实数区间均匀采样的时间发送。在该模型中，我们给出一个基于 BB84 的协议，该协议对任意有限联盟的 LOCC 对手保持安全，这些对手具有任意有限（可能指数级）的量子存储和纠缠。我们的构造也可以在离散时间模型中实例化。尽管先前的不可能性结果适用，我们能够获得一个信息论安全的 QPV 协议，其中诚实方的总资源（通信和存储）可以显著小于对手的资源界限。事实上，我们可以实现诚实方与对手资源之间的任何期望的多项式差距。据我们所知，文献中所有先前的协议要求诚实方的资源至少与对手的纠缠一样大。有趣的是，我们协议中诚实方与对手方资源之间的资源差距取决于时间测量的精度。随着最知名时钟的精度随着进一步研究而提高，我们协议中的资源差距不断增加。特别是，对手的资源界限不断增加，而诚实方的资源基本保持不变。我们称之为“我睡觉，你工作”范式。
英文摘要：
Position verification, introduced by Chandran et al. (SIAM J. Computing 2014), allows verifiers to test a prover's claimed position by an interactive protocol. Classical position verification is impossible. Even for Quantum Position Verification (QPV), there always exists an LOCC (Local Operations and Classical Communication) attack if the adversary can hold an exponentially large amount of preshared entanglement. Somewhat surprisingly, we show that we can circumvent this barrier in the idealized continuous-time model, where time is represented by a real-valued parameter and challenge messages can be sent at a time sampled uniformly from a real interval. In this model, we give a BB84-based protocol that remains secure against any finite coalition of LOCC adversaries with arbitrary finite (possibly exponential) quantum storage and entanglement. Our construction can also be instantiated in the discrete-time model. Even though the previous impossibility results apply, we are able to obtain an information-theoretic QPV protocol in which the honest parties' total resources (communication and storage) can be significantly smaller than the adversarial resource bound. In fact, we can achieve any desired polynomial gap between honest parties and adversarial resources. To our knowledge, all previous protocols in the literature required resources of the honest parties to be at least as large as the adversarial entanglement. Interestingly, the resource gap between the honest and adversarial party resources in our protocol depends on how precisely time can be measured. As the precision of the best-known clock improves with further research, the resource gap in our protocol keeps increasing. In particular, the adversarial resource bound keeps increasing while the honest parties' resources remain largely the same. We call this the "I sleep, you work" paradigm.
