STATISTICAL INTERFERENCE FOR QUANTUM SYSTEMS

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This highly interdisciplinary project is dedicated to the theoretical study and practical feasibility of biomedical applications of recently developed statistical decision procedures that operate on data known to be dominated by quantum-mechanical noise. The methodology has been successfully used over the last decade by electrical communications engineers, particularly those involved with quantum optics systems, and allows the statistician, for the first time, the opportunity to undertake nearly-classical statistical decision theory on data that, for example, are known to have, in principle no joint distribution. This latter, highly non-intuitive fact, and others that are equally well experimentally established, all have fundamental consequences for how statisticians must re-think the planning of experiments and data anlayses for processes occurring at the molecular level. This is especially important, for example, when the crucial experiments require, low power levels so as to not distort the true underlying biological processes (in which case not much data can be collected) or when important, but rare, events or markers must be sorted out from other sources of noise, including quantum noise. Of special biomedical interest are novel pairings of this quantum-consistent statistical theory and technologies in the rapidly developing field of light-based imaging devices and detection methods, and analysis techniques using other forms of radiation. Possible biomedical applications thus could include: reduced-dose PET scans; real-time, laser-based, reduced-illumination confocal microscopy of living cells and tissue. Also of interest are applications that involve bioluminescent molecular tagging and enhanced chemiluminescence, which would allow the non-invasive, non-destructive study of biological processes at the level of individual molecules and atoms. Moreover any of the relatively new fields of molecular electronics and electronics using super-lattices and quantum wells, and the manipulation of isolated trapped electons, ions, atoms, molecules or biological organisms, may provide the initial experimental contexts for optimal statistical estimatio and decision making, in the presence of quantum noise.