Constructing exact symmetric informationally complete measurements from numerical solutions

DOI10.1088/1751-8121/aab4cdzbMath1397.81022arXiv1703.05981OpenAlexW2606846634MaRDI QIDQ4565027

Tuan-Yow Chien, Marcus Appleby, Steven T. Flammia, Shayne F. D. Waldron

Publication date: 7 June 2018

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1703.05981

zbMATH Keywords

Galois symmetriesalgebraic number theorySICsinteger relation algorithm

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Quantum measurement theory, state operations, state preparations (81P15) Galois representations (11F80)

Related Items (28)

SIC-POVMs from Stark units: Prime dimensions n2 + 3 ⋮ SICs: some explanations ⋮ Dimension towers of SICS: II. Some constructions ⋮ SICs and the elements of order three in the Clifford group ⋮ Tight frames, Hadamard matrices and Zauner’s conjecture ⋮ Communication of partial ignorance with qubits ⋮ Equioverlapping measurements ⋮ Joint measurability of quantum effects and the matrix diamond ⋮ The Fourier transform of a projective group frame ⋮ Frames over finite fields: basic theory and equiangular lines in unitary geometry ⋮ Optimality of T-gate for generating magic resource ⋮ Welch bound equality sets with few distinct inner products from Delsarte-Goethals sets ⋮ Dimension towers of SICs. I. Aligned SICs and embedded tight frames ⋮ A new construction of approximately SIC-POVMs derived from Jacobi sums over finite fields ⋮ Aims and scope of the special issue ``Quantum foundations: informational perspective ⋮ Negativity bounds for Weyl-Heisenberg quasiprobability representations ⋮ SICs and algebraic number theory ⋮ Sporadic SICs and the normed division algebras ⋮ Two new constructions of approximately SIC-POVMs from multiplicative characters ⋮ Construction of \(\varepsilon_d\)-ASIC-POVMs via 2-to-1 PN functions and the Li bound ⋮ A short history of frames and quantum designs ⋮ New constructions of approximately SIC-POVMs via difference sets ⋮ Frame multiplication theory and a vector-valued DFT and ambiguity function ⋮ Entanglement properties of multipartite informationally complete quantum measurements ⋮ OPTIMAL LINE PACKINGS FROM FINITE GROUP ACTIONS ⋮ Moment Maps and Galois Orbits in Quantum Information Theory ⋮ Simplified exact SICS ⋮ Universal quantum computing and three-manifolds

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