W. van Dam and P. Hayden introduced the concept of state embezzlement and proved that in finite dimensions one could approximately embezzle states but not perfectly. We show that perfect embezzlement is still impossible in a tensor product framework even if one allows infinite dimensional resource spaces, but that perfect embezzlement is possible in a commuting operator framework. Our approach is to create a link between perfect embezzlement and the existence of special states on tensor products of the “universal C*-algebra of a non-commuting unitary".

Coauthors: R. Cleve, L. Liu, and S. Harris.