Mathematical aspects of continuous variable quantum information

量子信息理论试图定量地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，但它们的性质通常还不太清楚。连续变量系统的情况下，描述，例如，光纤通信信道，是特别相关的操作，但提出了重大的数学挑战。本项目旨在推进具有连续变量的量子信息理论。一方面，它将有助于缩小已知的经典信息理论与量子信息设置之间的差距：通过发现经典信息理论结果的非交换推广，这将为后者的普遍性提供新的亮点。另一方面，该项目将寻求识别本质上的量子特征，这些特征可以应用于加密协议等。将特别强调处理连续变量的特殊技术和操作后果，而不是有限维系统。

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.