Quantum Information Theory

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