Quantum Information Theory

玛丽·贝丝·鲁斯凯，马萨诸塞大学洛厄尔分校DMS-0203211摘要：***************************************************************This项目涉及到当量子粒子被用于处理和/或传输信息时出现的一些数学问题。P.I.计划继续分析和改进噪声模型；这些模型在量子通信和量子计算的误差分析中都很重要。量子通信的工作包括一项可能解决长期存在的问题的提议，即纠缠输入是否可以增强量子通道传输经典信息的能力。P.I.还计划构建新类别的纠错码，作为码的原型，这种码可以被设计成处理量子计算的特定实现最容易受到的错误。这样的代码可以与其他技术相结合，以减少总体代码长度。P.I.还将考虑一种随机哈密顿方法来分析提议的绝热量子计算方案的效率。最后，P.I.计划继续研究信息几何中的度量学，以及它们与纯度、相对熵和状态间距离的度量之间的联系。现在已经确定，量子粒子有可能为更强大的计算机和新的安全通信方法提供基础。尽管建造量子计算机仍然是一项艰巨的实验挑战，但几种量子通信和加密方法的可行性已经得到了令人信服的证明。然而，很明显，所有实用的乐器都是不完美的，容易受到噪音和错误的影响。这并不令人惊讶；处理噪音长期以来一直是古典交流的一个重要方面。然而，量子信息设备容易受到由噪声引起的更大、更复杂的各种误差的影响。这带来了新的数学挑战。这项提案解决了其中的一些问题。处理噪声的有效方法对于国家成功地将量子理论的力量用于下一代计算机和密码协议至关重要。***************************************************************--

PI: Mary Beth Ruskai, University of Massachusetts LowellDMS-0203211Abstract: ***************************************************************This project is concerned with a number of mathematical problemswhich arise when quantum particles are used to process and/ortransmit information. The P.I. plans to continue the analysis and refinement of models of noise; these are important in bothquantum communication and error analysis in quantum computation. Work in quantum communication includes a proposal which may resolvethe long-standing question of whether or not entangled inputs canenhance the capacity of quantum channels to transmit classicalinformation. The P.I. also plans to construct new classes of errorcorrecting codes as prototypes for codes which can be designed to deal with those errors to which a particular implementation of quantum computation is most vulnerable. Such codes couldbe combined with other techniques to reduced the overall codelength. The P.I. will also consider a random Hamiltonianapproach to the analysis of the efficiency of a proposed schemefor adiabatic quantum computation. Finally, the P.I. plans tocontinue the study of metrics in information geometry, and theirconnection to measures of purity, relative entropy, and distancesbetween states.It has now been established that quantum particles have the potentialto provide the basis for vastly more powerful computers, and new methodsof secure communication. Although building quantum computers remainsa formidable experimental challenge, the feasibility of several methodsof quantum communication and encryption have already been convincinglydemonstrated. However, it is also clear that all practical instrumentation is imperfect and subject to noise and errors.This is not surprising; dealing with noise has long been an importantfacet of classical communication. However, quantum information devicesare subject to a much larger and more complex variety of errors arisingfrom noise. This gives rise to new mathematical challenges. Thisproposal deals with a number of these questions. Effective methodsof dealing with noise are essential to the success of the nation'sability to exploit the power of quantum theory for next generation ofcomputers and cryptographic protocols. ***************************************************************--