A unified approach to SIC-POVMs and MUBs

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.

15 pages

References in corpus (5)

• SIC-POVMs and the Extended Clifford Group
• Mutually Unbiased Bases and Finite Projective Planes
• A SU(2) recipe for mutually unbiased bases
• State space structure and entanglement of rotationally invariant spin systems
• Simple Minimal Informationally Complete Measurements for Qudits

Cited by in corpus (12)

• The SIC Question: History and State of Play
• The Lie Algebraic Significance of Symmetric Informationally Complete Measurements
• Mutually unbiased bases: tomography of spin states and star-product scheme
• Symmetric informationally complete positive operator valued measure and probability representation of quantum mechanics
• Systems of Imprimitivity for the Clifford Group
• SU(2) and SU(1,1) Approaches to Phase Operators and Temporally Stable Phase States: Applications to Mutually Unbiased Bases and Discrete Fourier Transforms
• Miscellaneous Applications of Quons
• Unitary and Non-Unitary Matrices as a Source of Different Bases of Operators Acting on Hilbert Spaces
• On Two Ways to Look for Mutually Unbiased Bases
• Matrix reduction and Lagrangian submodules
• Bases for spin systems and qudits from angular momentum theory
• On mutually unbiased bases: Passing from d to d**2