A unified approach to SIC-POVMs and MUBs

2007/04/30 by Olivier Albouy, O. Albouy, M. Kibler +1 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Algebra over a field #Biology #Computer science #Gene #Genetics #Hilbert space #Mathematics #Matrix Theory and Algorithms #Mutually unbiased bases #Operator (biology) #Pure mathematics #Quantum Information and Cryptography #Quantum optics and atomic interactions #math-ph #math.MP #quant-ph

paper · pdf · doi:10.1007/s10946-007-0032-5

published as Journal of Russian Laser Research 28 (2007) 429-438 · 15 pages

arxiv created 2007/09/01 · openalex publication_date 2007/09/01 · arxiv updated 2011/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

A unified approach to (symmetric informationally complete) positive operator valued measures and mutually unbiased bases is developed in this article. The approach is based on the use of operator equivalents expanded in the enveloping algebra of SU(2). Emphasis is put on similarities and differences between SIC-POVMs and MUBs.

Citations

• Foundations of Quantum Mechanics, an Empiricist Approach
• SIMPLE MINIMAL INFORMATIONALLY COMPLETE MEASUREMENTS FOR QUDITS
• State space structure and entanglement of rotationally invariant spin systems
• Symmetric informationally complete quantum measurements
• A SU(2) RECIPE FOR MUTUALLY UNBIASED BASES
• Theory of Complex Spectra. II

Cited by

• Systems of Imprimitivity for the Clifford Group
• The Lie algebraic significance of symmetric informationally complete measurements