[论文解读] A Proposal for Quantum Fisher Information Optimization and its Relation with Entanglement Measures

Volkan Erol|arXiv (Cornell University)|May 12, 2017

Quantum Information and Cryptography参考文献 46被引用 9

一句话总结

该论文提出了一种在局部操作与经典通信（LOCC）下优化量子费舍尔信息（QFI）的框架，以研究其在两比特和量子比特-三重态系统中与纠缠度量的排序关系。关键发现是，在LOCC下最大化的QFI与两量子比特态的相对熵纠缠度量表现出一致的排序关系，表明QFI在特定情形下可作为纠缠的潜在代理指标。

ABSTRACT

Studies about Quantum Information Theory continue actively in many research institutions. Very recently, pratical setups of large scale quantum computers are widely studied e.g. quantum repeaters, memories and processors. Entanglement provides us a computational advantage in realization of quantum algorithms. Some ways to quantifiying entanglement were defined. The best formal way to quantify it, is the methods that we call Entanglement Measures or Entanglement Monotones. In this research area, State Ordering Problem is defined and still an open problem especially for multiparticle entangled states. Fisher Information provides a good background for the solution of some actual Information Theory problems. Quantum Fisher Information (QFI) is a value that could be used in situations where phase sensitivity is important and this concept is expected to be the quantum version of the mentioned inftrastructure for Quantum Systems. QFI cannot be defined as an Entaglement Measure or Monotone. In the scope of this thesis, a new optimization technique is proposed for optimizing QFI and thanks to this optimization method, the ordering relation between QFI and entanglement measures is studied. Based on the studies made in the area of quantum state ordering, new and interesting analysis results are found and reported. The main important and interesting result achieved is that for two qubit quantum states, QFI maximized under Local Operation and Classical Communication has an interesting ordering relation with entanglement measures especially with Relative Entropy of Entanglement. Our study is extended for the qubit-qutrit systems and ordering relations and classification results are presented. For some quantum systems, the changes in QFI under decoherence channels are also considered.

研究动机与目标

• 通过分析量子费舍尔信息（QFI）与纠缠度量之间的关系，解决多体纠缠态中的开放性‘态排序问题’。
• 开发一种新颖的LOCC下QFI优化技术，以实现与纠缠单调量的有意义比较。
• 研究尽管QFI并非纠缠度量，但在特定量子系统中是否可作为纠缠的可靠指标。
• 将分析扩展至量子比特-三重态系统，研究退相干下的排序与分类。
• 探索选定量子系统中QFI在退相干通道下的行为。

提出的方法

• 提出一种新的优化方法，以在LOCC约束下最大化QFI，从而实现与纠缠度量的比较。
• 采用相对熵纠缠度量作为比较基准，与优化后的QFI进行对比。
• 将优化框架应用于两量子比特和量子比特-三重态系统，以分析排序关系。
• 使用数值与解析技术评估QFI在各种退相干通道下的变化。
• 基于不同量子态下QFI与纠缠度量的排序关系，进行态分类。
• 基于一篇98页分析内容、包含37幅图表的博士论文框架，主要以土耳其语撰写，但附有英文摘要。

实验结果

研究问题

• RQ1 在两量子比特系统中，LOCC下最大化的量子费舍尔信息是否与既有的纠缠度量表现出一致的排序关系？
• RQ2 尽管QFI并非纠缠单调量，它是否可在特定量子态中作为纠缠的可靠代理？
• RQ3 QFI与纠缠度量之间的排序关系在更高维系统（如量子比特-三重态态）中如何推广？
• RQ4 QFI在不同退相干通道下的行为如何？其对QFI-纠缠排序关系有何影响？
• RQ5 所提出的优化方法是否能解决或揭示多体纠缠态中的‘态排序问题’？

主要发现

• 对于两量子比特态，LOCC下最大化的QFI与相对熵纠缠度量表现出一致且非平凡的排序关系。
• 研究表明，LOCC下QFI的优化可有效区分两量子比特系统中的纠缠特性，表明其作为纠缠代理的潜在应用价值。
• 在量子比特-三重态系统中，QFI与纠缠度量之间的排序关系得以保持，但分类模式更为复杂。
• 在退相干作用下，QFI值的变化与纠缠退化趋势相关，表明其对噪声具有敏感性。
• 结果支持LOCC下QFI优化可为量子态纠缠结构提供有意义的洞见。
• 该工作通过引入基于QFI的新分析框架，为解决‘态排序问题’的持续努力作出了贡献。