Product Bases in Quantum Information Theory

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We review the role of product bases in quantum information theory. We prove two conjectures which were made in DiVincenzo et al., quant-ph/9908070, namely the existence of two sets of bipartite unextendible product bases, in arbitrary dimensions, which are based on a tile construction. We pose some questions related to complete product bases.
9 pages, 4 figures; submitted to the Proceedings of the XIII International Congress on Mathematical Physics

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