Quantum Information and Quantum Foundations

1.量子信息理论中的各种问题将使用量子域中概率的一致性公式来解决，而不限于宏观事件或测量。一类问题涉及如何使用纠缠态资源、局域量子操作和各种类型的通信信道在空间分离的量子系统之间传输信息的各种特征。这些包括密集编码，酉运算和区分不同的量子态。第二类问题涉及量子纠错码的构建，用于量子信息的可靠传输和存储，以及更好地理解这些代码的基本原理。第三类，与前两类无关，涉及量子信息的基本性质：在哪些方面它不同于普通（香农）信息理论，在哪些方面它使用相同的原则，以及这种理解是否可以用于量子信息位置的定量估计。除了概率论和量子力学的标准方法外，计算机模拟将用于研究模型系统。更广泛的影响研究工作将有助于在麦基梅隆大学的教育计划在本科和研究生水平，通过提供研究项目的学生，包括那些工作的博士学位。博士后研究人员将有机会在参加这个研究小组的同时提高他们的技能，使他们成为科学界更有价值的成员。学生和博士后将参加正在进行的量子信息系列研讨会，以及涉及这些主题的偶尔课程，这两个课程都吸引了居住在匹兹堡的其他科学家和理科学生。量子力学和量子信息教学的改进最终将证明对匹兹堡以外的大学生以及本市的大学生都是有益的。

1. Intellectual meritVarious issues in quantum information theory will be addressed using a consistent formulation of probabilities in the quantum domain, one not limited to macroscopic events or measurements. One class of problems involves various features of how information can be transferred between spatially separated quantum systems using the resources of entangled states, local quantum operations, and various types of communication channel. These include things like dense coding, unitary operations, and distinguishing different quantum states. A second class of problems involves the construction of quantum error correcting codes for the reliable transmission and storage of quantum information, and a better understanding of the fundamental principles underlying such codes. A third class, not unrelated to the preceding two, involves the fundamental nature of quantum information: in what respects it is different from and in what respects it uses the same principles as ordinary(Shannon)information theory, and whether such understanding can be useful forquantitative estimates of the location of quantum information. In addition to the standard methods of probability theory and quantum mechanics, computer simulations will be used to study model systems.2. Broader impactsThe research effort will contribute to the education program at Carnegie-MellonUniversity at both the undergraduate and graduate levels through providing research projects for students, including those working towards a PhD. Postdoctoral research associates will have an opportunity to sharpen their skills while participating in this research group, making them more valuable members of the scientific community. Students and postdocs will take part in an ongoing seminar series in quantum information, and occasional courses which address these subjects, both of which attract other scientists and science students living in Pittsburgh. Improvements in teaching quantum mechanics and quantum information will eventually prove beneficial to university students outside Pittsburgh as well as those in this city.