Representation of uncertainty with quantum logic formulations

Quantum Logic, born of the attempts of J. von Neumann, P. Jordan, E. Wigner, and G. Birkhoff, to provide an axiomatic foundation for quantum mechanics, has lately been a subject of significant interest for its computing potential. Most recently, efforts in quantum computation, to resolve dilemmas created by uncertainties, have focused on increasing the efficiency of search and factorization algorithms. We suggest an addition to this list of information-theoretic applications of quantum mechanics -- the use of the logical paradigm underlying the theory of quantum mechanics for representing uncertainty, and devising computation strategies for problems in risk assessment. The examples we present specifically address risk issues involved in the transport of nuclear weapons. Our results indicate that for some classes of problems, certain quantum logic representations of uncertainty are exponentially more compact than the corresponding Boolean logic representations. For a subclass of these problems, the gain in compactness comes at the loss of some information. Interestingly, this result is very similar to a tradeoff involved in the Deutsch-Jozsa algorithm to solve the Deutsch problem in quantum computing. For another subclass of these problems, none of the given information is lost! The benefits of our work in knowledge representation using quantum logic can be realized even without the existence of any quantum mechanical computing device. Our work suggests that the theory of quantum mechanics has a practical applicability and usefulness that goes beyond analyzing quantum mechanical systems or quantum mechanical devices --Abstract, page iii