***************************************************************
This project is concerned with a number of mathematical problems which arise when quantum particles are used to process and/or transmit information. The P.I. plans to continue the analysis and refinement of models of noise; these are important in both quantum communication and error analysis in quantum computation. Work in quantum communication includes a proposal which may resolve the long-standing question of whether or not entangled inputs can enhance the capacity of quantum channels to transmit classical information. The P.I. also plans to construct new classes of error correcting 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 could be combined with other techniques to reduced the overall code length. The P.I. will also consider a random Hamiltonian approach to the analysis of the efficiency of a proposed scheme for adiabatic quantum computation. Finally, the P.I. plans to continue the study of metrics in information geometry, and their connection to measures of purity, relative entropy, and distances between states.
It has now been established that quantum particles have the potential to provide the basis for vastly more powerful computers, and new methods of secure communication. Although building quantum computers remains a formidable experimental challenge, the feasibility of several methods of quantum communication and encryption have already been convincingly demonstrated. 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 important facet of classical communication. However, quantum information devices are subject to a much larger and more complex variety of errors arising from noise. This gives rise to new mathematical challenges. This proposal deals with a number of these questions. Effective methods of dealing with noise are essential to the success of the nation's ability to exploit the power of quantum theory for next generation of computers and cryptographic protocols.
***************************************************************
--
