Locality Induced Non-Universality for Abelian Symmetries

Abstract

According to a well-known result in quantum computing, any unitary transformation on a composite system can be generated using $2$-local unitaries. Interestingly, this universality need not hold in the presence of symmetries. In this paper, we study the analogues of the non-universality results for all Abelian symmetries.

arXiv comment11 pages, 1 table, 0 figures