Abstract. Decompositions of the unitary group U(n) are useful tools in quantum information theory as they allow one to decompose unitary evolutions into local evolutions and evolutions causing entanglement. Several recursive decompositions have been proposed in the literature to express unitary operators as products of simple operators with properties relevant in entanglement dynamics. In this paper, using the concept of grading of a Lie algebra, we cast these decompositions in a unifying scheme and show how new recursive decompositions can be obtained. In particular, we propose a new recursive decomposition of the unitary operator on N qubits, and give a numerical example.

PACS numbers: 03.65.−w, 02.20.Tw, 03.65.Ud

Print publication: Issue 15 (18 April 2008)
Received 8 November 2007
Published 2 April 2008