[论文解读] Preparation contextuality: the ground of quantum communication advantage

Debashis Saha, Anubhav Chaturvedi|arXiv (Cornell University)|Feb 20, 2018

Quantum Computing Algorithms and Architecture被引用 3

一句话总结

本文确立了制备语境性（PC）作为通信任务中量子优势的基础非经典特征。通过构建与单向通信复杂性问题相关的无偏见通信协议，作者表明量子优势通过制备非语境性不等式的违背而得以操作性地揭示，且在关键问题上展示了无界的违背。

ABSTRACT

Where does quantum advantage spring from? Such an investigation necessitates invoking an ontology on which non-classical features of quantum theory are explored. One such non-classical ontic-feature is preparation contextuality (PC) and advantage in oblivious communication tasks is its operational signature. In this letter, we deal with quantum advantage in communication which has two prominent manifestations, advantage in communication complexity (CC) and device independent information processing based on violation of Bell inequalities. First, we demonstrate that quantum advantage in one-way CC operationally reveals PC. Specifically, we construct oblivious communication tasks tailored to one-way CC problems. The bound on classical success probability in the oblivious communication tasks forms our preparation non-contextual inequalities. We use the same states along with their orthogonal mixtures and measurements responsible for advantage in one-way CC problems to orchestrate an advantageous protocol for the oblivious communication tasks and the violation of the associated inequalities. Further, we find a criterion for unbounded violation of these inequalities and demonstrate the same for two widely studied CC problems. Second, we prove that (spatial and temporal) Bell-inequality violation implies an advantage in oblivious communication tasks, thereby revealing PC. Along with the implications of this work, we discuss other known indications towards our assertion that PC is the fundamental non-classical feature underlying quantum advantage.

研究动机与目标

• 识别通信任务中量子优势的本体论根源。
• 将单向通信复杂性（CC）中的量子优势与制备语境性（PC）联系起来。
• 证明贝尔不等式违背意味着在无偏见通信任务中存在优势，从而揭示PC。
• 确立PC作为支撑量子通信优越性的基本资源。
• 为制备非语境性不等式的无界违背提供操作性标准。

提出的方法

• 从单向CC问题构造定制的无偏见通信任务，以探测量子优势。
• 从这些任务中经典成功概率的界推导出制备非语境性不等式。
• 使用使CC优势成为可能的相同量子态、其正交混合态以及测量来实现量子协议。
• 证明量子协议违背所推导出的制备非语境性不等式，从而揭示PC。
• 证明空间和时间上的贝尔不等式违背意味着在无偏见通信任务中存在优势。
• 利用已知的CC问题建立制备非语境性不等式无界违背的标准。

实验结果

研究问题

• RQ1 单向通信复杂性中的量子优势能否在操作上与制备语境性联系起来？
• RQ2 制备非语境性不等式的违背是否可作为无偏见通信任务中量子优势的标志？
• RQ3 是否存在一个用于量子通信中制备非语境性不等式无界违背的标准？
• RQ4 能否证明贝尔不等式违背意味着在无偏见通信任务中存在优势，从而揭示PC？
• RQ5 制备语境性是否是支撑量子通信优势的根本非经典特征？

主要发现

• 单向通信复杂性中的量子优势通过制备非语境性不等式的违背，操作性地揭示了制备语境性。
• 使CC问题中实现优势的相同量子态和测量，也能在无偏见通信任务中实现成功协议，并违背所推导出的不等式。
• 建立并展示了针对两个广泛研究的通信复杂性问题的制备非语境性不等式无界违背的一般标准。
• 空间和时间贝尔不等式的违背意味着在无偏见通信任务中存在优势，从而揭示了制备语境性。
• 本文提供了强有力的证据，表明制备语境性是支撑量子通信优势的根本非经典特征。
• 结果将量子优势的不同表现形式——通信复杂性和设备无关信息处理——统一于制备语境性的共同框架之下。