违反贝尔不等式：当你失去量子系统时该怎么办
Violating a Bell Inequality: What to Do When You Lose Your Quantum System
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中文总结 AI 辅助
本文研究贝尔实验中量子系统丢失时的最优回退策略，证明CHSH不等式存在对所有效率最优的策略，但一般情况策略随效率变化，可降低关闭探测漏洞的要求。
中文摘要 AI 辅助
探测漏洞是贝尔非局域性中一个众所周知的漏洞，其动机源于贝尔实验中使用的探测器效率低下。然而，这种低效率实际上是任何用于量子网络的光子平台的普遍特征，因为光子很容易被周围环境吸收。当量子系统（通常是光子）丢失时，各方应输出什么？最自然的选择是退回到一种确定性策略，其中每一方通过其本地输入的函数产生输出。在本文中，我们研究了如何针对不同效率$\eta$为一般贝尔不等式选择这种回退策略，以最大化可能的违反。我们在数学上证明，对于CHSH不等式，存在一种对所有$\eta$都最优的回退策略。然而，在一般情况下，我们发现最优回退策略可能随$\eta$变化，有时以令人惊讶的方式变化。例如，我们找到一个贝尔不等式的例子，其中接近阈值效率的最优回退策略并非无损环境中的最优确定性策略。我们的结果可以降低关闭探测漏洞的效率要求，因此对于贝尔不等式违反的应用（如量子心灵感应或设备无关量子密钥分发）很有用。
英文摘要
The detection loophole is a well-known loophole in Bell nonlocality motivated by the inefficiency of detectors used in Bell experiments. However, this inefficiency is actually a ubiquitous feature of any photonic platform for quantum networks since photons are readily absorbed by the surrounding environment. When the quantum system, usually a photon, is lost, what should the parties output? The most natural choice is to fall back to a deterministic strategy where each party produces an output via a function of her local input. In this paper, we study how to choose such a fallback strategy for general Bell inequalities with respect to different efficiencies $η$ to maximize the possible violation. We mathematically prove that for the CHSH inequality, there exists a fallback strategy that is optimal for all $η$. However, in general, we find that the optimal fallback strategy can vary with $η$, sometimes in surprising ways. For example, we find an example of a Bell inequality where the optimal fallback strategy near the threshold efficiency is not an optimal deterministic strategy in the lossless setting. Our results can reduce the efficiency requirements for closing the detection loophole and thus are useful for applications of Bell inequality violation, such as quantum telepathy or device-independent quantum key distribution.
发表机构
- Shanghai Institute for Mathematics and Interdisciplinary Sciences (SIMIS)（上海数学与交叉学科研究院）
- Research Institute of Intelligent Complex Systems, Fudan University（复旦大学复杂系统研究所）
- Yau Mathematical Sciences Center, Tsinghua University（清华大学丘成桐数学科学中心）
- Department of Computer Science, University of Pittsburgh（匹兹堡大学计算机科学系）
- Department of Electrical and Computer Engineering, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校电气与计算机工程系）
- Center for Mathematics and Interdisciplinary Sciences, Fudan University（复旦大学数学与交叉科学中心）
- Beijing Institute of Mathematical Sciences and Applications (BIMSA)（北京国际数学研究中心）
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