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We introduce a model of computation based on read only memory (ROM), which allows us to compare the space-efficiency of reversible, error-free classical computation with reversible, error-free quantum computation. We show that a ROM-based quantum computer with one writable qubit is universal, whilst two writable bits are required for a universal classical… (More)

Let K be a full-dimensional convex subset of R n. We describe a new polynomial-time Turing reduction from the weak separation problem for K to the weak optimization problem for K that is based on a geometric heuristic. We compare our reduction, which relies on analytic centers, with the standard, more general reduction.

Let K be a convex subset of R n containing a ball of finite radius centered at c 0 and contained in a ball of finite radius R. We give an oracle-polynomial-time algorithm for the weak separation problem for K given an oracle for the weak optimization problem for K. This is done by reducing the weak separation problem for K to the convex feasibility… (More)

It appears, in principle, that the laws of quantum mechanics allow a quantum computer to solve certain mathematical problems more rapidly than can be done using a classical computer. However, in order to build such a quantum computer a number of technological problems need to be overcome. A stepping stone to this goal is the implementation of relatively… (More)

This short note describes a method to tackle the (bipartite) quantum separability problem. The method can be used for solving the separability problem in an experimental setting as well as in the purely mathematical setting. The idea is to invoke the following characterization of entangled states: A state is entangled if and only if there exists an… (More)

This dissertation is the result of my own work and includes nothing which is the outcome of work done in collaboration except where speciically indicated in the Acknowledgements. Abstract Ever since entanglement was identiied as a computational and cryptographic resource, eeort has been made to nd an eecient way to tell whether a given density matrix… (More)

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