Mehmet Dağlı et al 2008 J. Phys. A: Math. Theor. 41 155302 doi:10.1088/1751-8113/41/15/155302
A general framework for recursive decompositions of unitary quantum evolutions
Mehmet Dağlı, Domenico D'Alessandro and Jonathan D H Smith
Show affiliationsDecompositions 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
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03.67.Mn Entanglement measures, witnesses, and other characterizations
03.67.Lx Quantum computation architectures and implementations
- MSC
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22E60 Lie algebras of Lie groups (For the algebraic theory of Lie algebras, see 17Bxx)
22D10 Unitary representations of locally compact groups
81R15 Operator algebra methods (See also 46Lxx, 81T05)
81P68 Quantum computation and quantum cryptography (See also 68Q05, 94A60)
81R50 Quantum groups and related algebraic methods (See also 16W35, 17B37)
- Subjects
- Dates
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Issue 15 (18 April 2008)
Received 8 November 2007
Published 2 April 2008
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A general framework for recursive decompositions of unitary quantum evolutions
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