[论文解读] Why standard entanglement theory is inappropriate for the study of Bell scenarios

David Schmid|arXiv (Cornell University)|Apr 30, 2020

Quantum Mechanics and Applications被引用 12

一句话总结

本文主张在贝尔实验场景中研究非局域性时，局域操作与共享随机性（LOSR）比局域操作与经典通信（LOCC）更适合作为资源理论的框架。通过以LOSR替代LOCC，本文解决了长期存在的悖论，例如部分纠缠态的非局域性超过最大纠缠态的现象；提出了一个自然的真正多体纠缠概念；并实现了一个更简化、更通用的自检测框架。

ABSTRACT

A standard approach to quantifying resources is to determine which operations on the resources are freely available and to deduce the ordering relation among the resources that these operations induce. If the resource of interest is the nonclassicality of the correlations embodied in a quantum state, that is, entanglement, then it is typically presumed that the appropriate choice of free operations is local operations and classical communication (LOCC). We here argue that, in spite of the near-universal endorsement of the LOCC paradigm by the quantum information community, this is the wrong choice for one of the most prominent applications of entanglement theory, namely, the study of Bell scenarios. The nonclassicality of correlations in such scenarios, we argue, should be quantified instead by local operations and shared randomness (LOSR). We support this thesis by showing that various perverse features of the interplay between entanglement and nonlocality are merely an artifact of the use of LOCC-entanglement and that the interplay between LOSR-entanglement and nonlocality is natural and intuitive. Specifically, we show that the LOSR paradigm (i) provides a resolution of the anomaly of nonlocality, wherein partially entangled states exhibit more nonlocality than maximally entangled states, (ii) entails a notion of genuine multipartite entanglement that is distinct from the conventional one and which is free of several of its pathological features, and (iii) makes possible a resource-theoretic account of the self-testing of entangled states which simplifies and generalizes prior results. Along the way, we derive some fundamental results concerning the necessary and sufficient conditions for convertibility between pure entangled states under LOSR and highlight some of their consequences, such as the impossibility of catalysis for bipartite pure states.

研究动机与目标

• 挑战在贝尔实验场景中，将LOCC作为纠缠理论中自由操作的标准用法。
• 证明基于LOCC的纠缠理论在非局域性研究中会导致反直觉且病态的特征。
• 确立局域操作与共享随机性（LOSR）作为量化贝尔实验场景中非经典关联的适当自由操作。
• 解决非局域性悖论，即部分纠缠态的非局域性强于最大纠缠态的现象。
• 开发一种更简化、更通用的资源理论框架，用于纠缠态的自检测。

提出的方法

• 通过将自由操作集从LOCC替换为LOSR，重新诠释贝尔实验场景中非经典关联的资源理论。
• 分析在LOSR下纯纠缠态之间的可转换性，推导出此类变换的必要与充分条件。
• 将LOSR框架应用于研究两体与多体态的非局域性，特别关注部分纠缠态与最大纠缠态的行为差异。
• 利用LOSR框架重新推导并推广基于非局域关联的量子态自检测结果。
• 证明在LOSR下，两体纯态的催化作用不可能实现，这与基于LOCC的理论形成鲜明对比。
• 在LOSR下建立一种新的真正多体纠缠概念，避免了标准LOCC基定义中的病态特征。

实验结果

研究问题

• RQ1 为何标准的基于LOCC的纠缠理论无法为贝尔实验场景中的非局域性提供直观的解释？
• RQ2 为何将自由操作集从LOCC替换为LOSR能解决非局域性悖论，即部分纠缠态比最大纠缠态更非局域的现象？
• RQ3 在LOSR操作下，将一个纯纠缠态转化为另一个的必要与充分条件是什么？
• RQ4 LOSR框架能否支持一种更简化、更通用的纠缠态自检测协议？
• RQ5 基于LOSR的真正多体纠缠概念与传统的基于LOCC的定义有何不同，又如何实现改进？

主要发现

• LOSR框架通过表明部分纠缠态的非局域性并非病态，而是正确资源理论下的自然结果，从而解决了非局域性悖论。
• 基于LOSR的真正多体纠缠概念与标准LOCC基定义不同，且避免了后者存在的多种病态特征。
• 在LOSR下，两体纯态的催化作用不可能实现，这一结果与LOCC基理论中催化可能的情况形成鲜明对比，凸显了两种资源理论的根本差异。
• 本文推导出在LOSR下纯纠缠态之间可转换性的必要与充分条件，完整刻画了此类变换。
• LOSR框架支持一种更简化、更通用的资源理论自检测方法，涵盖了并扩展了先前的研究成果。
• LOSR基纠缠与非局域性之间的相互作用自然且直观，与LOCC基纠缠引发的反直觉特征形成鲜明对比。