Quantum Information Theory

这项研究项目是关于在描述有噪声的量子系统时出现的数学问题。其中一些工作解决了纠缠何时可以提高噪声量子通道的容量的问题。这包括对长期存在的猜想和有关算子空间的相关问题的研究。该项目还研究了除了熟悉的稳定器码之外的量子纠错的各个方面。最后，这项工作解决了绝热量子计算中出现的几个数学问题，并可能揭示绝热量子优化能否在多项式时间内解决难题这一有争议的问题。brbr物理学家在证明量子系统可用于新的密码学、通信和计算方法方面取得了相当大的进展。进一步发展高效、实用的量子通信系统需要进行类似于经典通信理论中关于信道容量和纠错的基础性工作的理论研究。这个项目研究了几个这样的数学问题，这些问题直接与量子信息处理的实际实现有关。

This research project is concerned with mathematical problems that arise in the description of noisy quantum systems. Some of the work addresses the question of when entanglement can enhance the capacity of a noisy quantum channel. This includes work on longstanding conjectures and related questions about operator spaces. The project also investigates aspects of quantum error correction beyond the familiar stabilizer codes. Finally, the work addresses several mathematical questions that arise in adiabatic quantum computation and may shed light on the controversial issue of whether or not adiabatic quantum optimization can solve hard problems in polynomial time.brbrPhysicists have made considerable progress in demonstrating that quantum systems can be used for new methods of cryptography, communication, and computation. Further development of efficient, practical quantum communication systems requires theoretical investigations analogous to the fundamental work in classical communication theory on channel capacity and error correction. This project investigates several such mathematical issues directly connected to the practical implementation of quantum information processing.