Product Bases in Quantum Information Theory

Abstract

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

References in corpus (3)

• Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
• Quantum Nonlocality without Entanglement
• Unextendible Product Bases and Bound Entanglement

Cited by in corpus (4)

• Unextendible Product Bases, Uncompletable Product Bases and Bound Entanglement
• Entangled states with positive partial transpose arising from indecomposable positive linear maps
• The geometry of entanglement witnesses and local detection of entanglement
• Entanglement Distillation; A Discourse on Bound Entanglement in Quantum Information Theory