Mathematical aspects of continuous variable quantum information

连续可变量子信息的数学方面

• 批准号: 318917567
• 负责人: Professor Dr. Robert König
• 金额: --
• 依托单位: Lehrstuhl Mathematische Physik (M5)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2018-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/318917567?language=en
• 关键词: Mathematical; aspects; continuous; variable; quantum

Quantum information theory seeks to quantitatively asses the potential of quantum-mechanical systems to act as information-processing resources. Relevant operational tasks include the preservation and transmission of classical information as well as quantum states. Corresponding mathematical optimization problems have been identified successfully, but their properties are poorly understood in general. The case of continuous-variable systems, which describe, e.g., fiberoptic communication channels, is particularly relevant operationally, but poses significant mathematical challenges.This project aims to advance quantum information theory with continuous variables. On the one hand, it will help to close the gap between what is known in classical information theory and the setting of quantum information: by finding non-commutative generalizations of classical information-theoretic results, this will shed new light on the generality of the latter. On the other hand, the project will seek to identify intrinsically quantum features, which have applications to e.g., cryptographic protocols. Special emphasis will be placed on the particular technical and operational consequences of dealing with continuous variables as opposed to finite-dimensional systems.

量子信息理论致力于定量评估量子力学系统作为信息处理资源的潜力。相关的操作任务包括保存和传输经典信息以及量子态。相应的数学优化问题已经被成功地识别出来，但对它们的性质一般了解得很少。描述光纤通信信道的连续变量系统在操作上具有特别重要的意义，但也提出了重大的数学挑战。该项目旨在用连续变量来推进量子信息理论。一方面，这将有助于缩小经典信息论中已知的东西与量子信息设置之间的差距：通过寻找经典信息论结果的非对易推广，这将为后者的普遍性提供新的曙光。另一方面，该项目将寻求识别本质上的量子特征，这些特征可应用于例如密码协议。将特别强调处理连续变量而不是有限维系统的特殊技术和业务后果。

项目成果

Uncertainty relations: An operational approach to the error-disturbance tradeoff

不确定性关系：误差与干扰权衡的操作方法

• DOI: 10.22331/q-2017-07-25-20
• 发表时间: 2017
• 作者: Joseph M. Renes;Volkher B. Scholz;Stefan Huber
• 通讯作者: Stefan Huber

The conditional Entropy Power Inequality for quantum additive noise channels

量子加性噪声通道的条件熵幂不等式

• DOI: 10.1063/1.5027495
• 发表时间: 2018
• 期刊: ArXiv
• 作者: Giacomo De Palma;Stefan Huber
• 通讯作者: Stefan Huber

Generalized Log-Majorization and Multivariate Trace Inequalities

广义对数极大化和多元迹不等式

• DOI: 10.1007/s00023-017-0569-y
• 发表时间: 2017
• 期刊: Annales Henri Poincaré
• 作者: Fumio Hiai;Robert König;Marco Tomamichel
• 通讯作者: Marco Tomamichel

Geometric inequalities from phase space translations

• DOI: 10.1063/1.4974224
• 发表时间: 2017-01-01
• 期刊: JOURNAL OF MATHEMATICAL PHYSICS
• 影响因子: 1.3
• 作者: Huber, Stefan;Koenig, Robert;Vershynina, Anna
• 通讯作者: Vershynina, Anna