Elliptical range theorems for generalized numerical ranges of quadratic operators

DOI10.1216/RMJ-2011-41-3-813zbMath1231.47003arXiv1102.1618MaRDI QIDQ633921

Nung-Sing Sze, Chi-Kwong Li, Yiu-Tung Poon, Hiroyuki Tomita, Mikio Nakahara

Publication date: 2 August 2011

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1102.1618

zbMATH Keywords

\(c\)-numerical rangeessential numerical rangequantum error correctionquadratic operator\(q\)-numerical rangeDavis-Wielandt shellhigher-rank numerical rangehigher rank numerical range\(k\)-numerical rangemixed unitary channeloperator quantum error correction

Mathematics Subject Classification ID

Quantum computation (81P68) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Numerical range, numerical radius (47A12) Other types of codes (94B60) Arithmetic codes (94B40)

Related Items

Higher dimensional numerical range of Lie products on self-adjoint operators ⋮ On the boundary of rank-knumerical ranges ⋮ The inverse \(q\)-numerical range problem and connections to the Davis-Wielandt shell and the pseudospectra of a matrix ⋮ Error correction schemes for fully correlated quantum channels protecting both quantum and classical information ⋮ Norm-parallelism of Hilbert space operators and the Davis-Wielandt Berezin number ⋮ On the Davis–Wielandt radius inequalities of Hilbert space operators ⋮ Maximal noiseless code rates for collective rotation channels on qudits ⋮ Multiplicative maps preserving the higher rank numerical ranges and radii ⋮ On the boundary of weighted numerical ranges ⋮ The \(c\)-numerical range of operator products on \({\mathcal{B}}(H)\) ⋮ Diagonals of operators and Blaschke’s enigma

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