Quantum Information Theory

量子信息论

• 批准号: 0314228
• 负责人: Mary Beth Ruskai
• 金额: --
• 依托单位: Tufts University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-01-01 至 2006-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0314228&HistoricalAwards=false
• 关键词: Quantum; Information; Theory

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

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. P.I.计划继续对噪声模型进行分析和完善；这些在量子计算中的Quantum沟通和错误分析中很重要。 量子通信中的工作包括一项提案，该提案可能会解决长期存在的问题，即是否纠缠了输入量是否纠缠了量子通道传递经典信息的能力。 P.I.还计划构建新类别的错误校正代码作为代码的原型，这些代码旨在处理那些量子计算的特定实现最脆弱的错误。 这样的代码可以与其他技术相结合以降低整体代码长度。 P.I.还将考虑随机的汉密尔顿攻击，以分析用于绝热量子计算的拟议方案的效率。 最后，P.I.计划在信息几何形状中的指标进行研究，并与纯度，相对熵和距离之间的衡量标准进行了联系。现在已经确定，量子粒子具有为更强大的计算机提供基础的潜力，以及新的方法。 尽管构建量子计算机仍然是巨大的实验挑战，但量子通信和加密方法的可行性已经令人信服。 但是，也很明显，所有实用的仪器都是不完美的，并且会受到噪音和错误的影响。这并不奇怪。长期以来，处理噪音一直是古典交流的重要方面。 但是，量子信息设备会遭受更大且更复杂的误差，从噪声引起。 这引起了新的数学挑战。 此功能涉及许多此类问题。 处理噪声的有效方法对于国家为下一代计算机和加密协议的利用量子理论的力量的成功至关重要。 ************************************************************************