Quantum Information Theory

主要研究者：玛丽贝丝Ruskai，马萨诸塞州洛厄尔大学DMS-0203211摘要：* 私家侦探计划继续分析和改进噪声模型;这些在量子通信和量子计算中的错误分析中都很重要。 量子通信的工作包括一项提案，该提案可能解决纠缠输入是否可以增强量子信道传输经典信息的能力的长期问题。 私家侦探他还计划构建新的纠错码类作为代码的原型，这些代码可以被设计为处理量子计算的特定实现最容易受到的错误。 这种编码可以与其他技术相结合，以减少总的编码长度。 私家侦探也将考虑一个随机哈密顿方法来分析绝热量子计算的效率。 最后私家侦探计划继续研究信息几何中的度量，以及它们与纯度、相对熵和状态间距离的关系。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。 尽管量子计算机的构建面临着巨大的实验挑战，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，所有的实际仪器都是不完美的，并且容易受到噪声和错误的影响，这也是很清楚的。这并不奇怪，处理噪声一直是经典通信的一个重要方面。 然而，量子信息设备会受到噪声引起的更大、更复杂的错误的影响。 这给数学带来了新的挑战。 本建议涉及其中一些问题。 有效的处理噪声的方法对于国家成功利用量子理论的力量用于下一代计算机和密码协议的能力至关重要。 ***************************************************************--

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. ***************************************************************--