[论文解读] Bell's Inequalities: Foundations and Quantum Communication

Časlav Brukner, Marek Żukowski|ArXiv.org|Sep 14, 2009

Quantum Mechanics and Applications参考文献 46被引用 5

一句话总结

本文建立了量子非定域性与通信协议中量子优势之间的基础性联系，表明贝尔不等式的违背和量子互补性是量子随机访问码、通信复杂性和量子计算中性能提升的关键资源。研究证明，由于时间贝尔不等式的违背，量子策略优于所有经典隐变量模型，甚至包括拥有无限经典资源的模型。

ABSTRACT

Efforts to construct deeper, realistic, level of physical description, in which individual systems have, like in classical physics, preexisting properties revealed by measurements are known as hidden-variable programs. Demonstrations that a hidden-variable program necessarily requires outcomes of certain experiments to disagree with the predictions of quantum theory are called "no-go theorems". The Bell theorem excludes local hidden variable theories. The Kochen-Specker theorem excludes noncontextual hidden variable theories. In local hidden-variable theories faster-that-light-influences are forbidden, thus the results for a given measurement (actual, or just potentially possible) are independent of the settings of other measurement devices which are at space-like separation. In noncontextual hidden-variable theories the predetermined results of a (degenerate) observable are independent of any other observables that are measured jointly with it. It is a fundamental doctrine of quantum information science that quantum communication and quantum computation outperforms their classical counterparts. If this is to be true, some fundamental quantum characteristics must be behind better-than-classical performance of information processing tasks. This chapter aims at establishing connections between certain quantum information protocols and foundational issues in quantum theory. After a brief discusion of the most common misinterpretations of Bell's theorem and a discussion of what its real meaning is, it will be demonstrated how quantum contextuality and violations of local realism can be used as useful resources in quantum information applications.

研究动机与目标

• 阐明贝尔不等式和互补性在量子信息协议中的基础性作用。
• 证明通信任务中量子优势的根源在于局域实在性和非互补性假设的违背。
• 表明量子随机访问码优于所有经典隐变量模型，即使在拥有无限经典资源的情况下，其优势源于时间贝尔不等式的违背。
• 研究量子非定域性与量子计算能力之间的联系，尤其在测量基于模型中的表现。
• 识别出超越纯纠缠之外的非经典特性，这些特性是量子计算加速的根本原因。

提出的方法

• 使用 Schmidt 分解分析两量子比特纠缠态，识别其非可分结构。
• 应用时间贝尔不等式建立量子随机访问码的模型，比较量子与经典隐变量策略。
• 构建一个能够模拟量子协议但遵守局域性和非互补性假设的隐变量模型。
• 证明量子协议违背时间贝尔不等式，而经典模型在成功概率 3/4 处达到上限。
• 分析基于测量的量子计算（如簇态），并展示其违背贝尔不等式，将其与非经典资源联系起来。
• 将量子协议与经典模拟进行比较，以分离非定域性和互补性在计算加速中的作用。

实验结果

研究问题

• RQ1 贝尔不等式的违背如何作为量子通信优势的资源？
• RQ2 量子随机访问码是否能超越所有经典隐变量模型，即使拥有无限经典资源？
• RQ3 互补性和非定域性在实现通信复杂性中量子优势方面起什么作用？
• RQ4 基于测量的量子计算与贝尔不等式违背之间有何关联？
• RQ5 为何过少或过多的纠缠均不足以实现强大的量子计算？

主要发现

• 量子随机访问码的成功概率超过 3/4，违背时间贝尔不等式，而经典隐变量模型的上限为 3/4。
• 时间贝尔不等式的违背表明，量子策略优于所有局域实在性模型，即使在使用任意大经典系统的情况下亦然。
• 违背贝尔不等式的纠缠态可实现纯态纠缠的浓缩，并确保量子密钥分发的安全性。
• 测量基量子计算中使用的簇态违背贝尔不等式，表明非定域性是量子计算能力的关键资源。
• 通信复杂性和量子博弈等协议中的量子优势，其根本根源在于局域实在性和互补性的违背。
• 本文识别出，纠缠不足或过量均会阻碍量子计算加速，表明纠缠与计算能力之间存在非单调关系。