RelativeC-numerical ranges for applications in quantum control and quantum information

DOI10.1080/03081080701535898zbMath1134.81012arXivmath-ph/0702005OpenAlexW1977718664MaRDI QIDQ5443472

Gunther Dirr, Uwe R. Helmke, Th. Schulte-Herbrüggen, Martin Kleinsteuber

Publication date: 21 February 2008

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0702005

zbMATH Keywords

generalized \(C\)-numerical rangesrelative \(C\)-numerical rangessymmetry of unitary orbits

Mathematics Subject Classification ID

Quantum computation (81P68) Numerical range, numerical radius (47A12)

Related Items (11)

Numerical ranges of tensors ⋮ Research problems on numerical ranges in quantum computing ⋮ Preservers of restricted unitary orbits of projections ⋮ Product numerical range in a space with tensor product structure ⋮ Partial isospectrality of a matrix pencil and circularity of the \(c\)-numerical range ⋮ Isospectrality and matrices with concentric circular higher rank numerical ranges ⋮ Lie-semigroup structures for reachability and control of open quantum systems: Kossakowski-Lindblad generators form Lie wedge to Markovian channels ⋮ GRADIENT FLOWS FOR OPTIMIZATION IN QUANTUM INFORMATION AND QUANTUM DYNAMICS: FOUNDATIONS AND APPLICATIONS ⋮ The significance of theC-numerical range and the localC-numerical range in quantum control and quantum information ⋮ Local Numerical Range for a Class of 2 ⊗ d Hermitian Operators ⋮ Restricted numerical range: A versatile tool in the theory of quantum information

Cites Work

• Elementary inclusion relations for generalized numerical ranges
• On the \(C\)-numerical range of a matrix
• Gradient flows computing the C-numerical range with applications in NMR spectroscopy
• Computer generated numerical ranges and some resulting theorems
• TheC-numerical range of matrices is star-shaped
• Another proof of a result of Westwick
• A theorem on numerical range
• C-numerical ranges andC-numerical radii
• The significance of theC-numerical range and the localC-numerical range in quantum control and quantum information
• Induced operators on symmetry classes of tensors

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