A General Framework for Recursive Decompositions of Unitary Quantum Evolutions

Details A General Framework for Recursive Decompositions of Unitary Quantum Evolutions A General Framework for Recursive Decompositions of Unitary Quantum Evolutions

2007-01-26

arxiv.org/abs/quant-ph/0701193v2

Physics

Quantum Physics

17 pages. To appear in J. Phys. A: Math. Theor. This article replaces our earlier preprint "A Recursive Decomposition of Unita

Scientific paper

10.1088/1751-8113/41/15/155302

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 we give a numerical example.

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