Achieving the orthoplex bound and constructing weighted complex projective 2-designs with Singer sets

DOI10.1016/j.laa.2016.09.005zbMath1348.42031arXiv1509.05333OpenAlexW2963573456MaRDI QIDQ331153

Bernhard G. Bodmann, John I. Haas

Publication date: 26 October 2016

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

Full work available at URL: https://arxiv.org/abs/1509.05333

zbMATH Keywords

relative difference setsdifference setsline packingsorthoplex boundprojective designsWelch bound

Mathematics Subject Classification ID

Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35) General harmonic expansions, frames (42C15) Quantum state estimation, approximate cloning (81P50)

Related Items (15)

Equiangular tight frames that contain regular simplices ⋮ Hadamard equiangular tight frames ⋮ Toward the classification of biangular harmonic frames ⋮ The core of a Grassmannian frame ⋮ Optimal arrangements of classical and quantum states with limited purity ⋮ Maximal orthoplectic fusion frames from mutually unbiased bases and block designs ⋮ A short history of frames and quantum designs ⋮ Low coherence unit norm tight frames ⋮ Constructions of biangular tight frames and their relationships with equiangular tight frames ⋮ Packings in Real Projective Spaces ⋮ Harmonic equiangular tight frames comprised of regular simplices ⋮ Constructing subspace packings from other packings ⋮ OPTIMAL LINE PACKINGS FROM FINITE GROUP ACTIONS ⋮ Unnamed Item ⋮ A Notion of Optimal Packings of Subspaces with Mixed-Rank and Solutions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Complex equiangular tight frames and erasures
• The road to deterministic matrices with the restricted isometry property
• Complex equiangular cyclic frames and erasures
• Painless reconstruction from magnitudes of frame coefficients
• Equiangular lines in \(C^r\). II
• Grassmannian frames with applications to coding and communication
• Optimal frames for erasures.
• Nonlinear functions in abelian groups and relative difference sets.
• Finite geometry and character theory
• A new proof for the existence of mutually unbiased bases
• A partial derandomization of phaselift using spherical designs
• Frames, graphs and erasures
• Equiangular lines, mutually unbiased bases, and spin models
• A fourier analytic approach to the problem of mutually unbiased bases
• QUANTUM DESIGNS: FOUNDATIONS OF A NONCOMMUTATIVE DESIGN THEORY
• UNITARY OPERATOR BASES
• Tight informationally complete quantum measurements
• Tomography of Quantum States in Small Dimensions
• Weighted complex projective 2-designs from bases: Optimal state determination by orthogonal measurements
• Sphere-packing bounds in the Grassmann and Stiefel manifolds
• Grassmannian beamforming for multiple-input multiple-output wireless systems
• Achieving the Welch Bound With Difference Sets
• Lower bounds on the maximum cross correlation of signals (Corresp.)
• Packing Lines, Planes, etc.: Packings in Grassmannian Spaces
• Symmetric informationally complete quantum measurements
• Symmetric informationally complete positive-operator-valued measures: A new computer study
• Kirkman Equiangular Tight Frames and Codes
• The Closest Packing of Spherical Caps in n Dimensions
• Equiangular lines in \({\mathbb{C}}^r\)

This page was built for publication: Achieving the orthoplex bound and constructing weighted complex projective 2-designs with Singer sets