An operational link between MUBs and SICs

Abstract

We exhibit an operational connection between mutually unbiased bases and symmetric infomationally complete positive operator-valued measures. Assuming that the latter exists, we show that there is a strong link between these two structures in all prime power dimensions. We also demonstrate that a similar link cannot exists in dimension 6.

17 pages, 2 figures

References in corpus (6)

• On mutually unbiased bases
• SIC-POVMs: A new computer study
• Numerical evidence for the maximum number of mutually unbiased bases in dimension six
• Mutually unbiased bases, orthogonal Latin squares, and hidden-variable models
• The monomial representations of the Clifford group
• Radon Transform in Finite Dimensional Hilbert Space

Cited by in corpus (11)

• The SIC Question: History and State of Play
• Mutually unbiased bases and symmetric informationally complete measurements in Bell experiments
• Nonlocality, steering and quantum state tomography in a single experiment
• Mutually unbiased frames
• Enhanced Schmidt number criteria based on correlation trace norms
• States that "look the same" with respect to every basis in a mutually unbiased set
• tqix: A toolbox for Quantum in X: Quantum measurement, quantum tomography, quantum metrology, and others
• Testing incompatibility of quantum devices with few states
• Uncertainty relations for unified ($\alpha$,$\beta$)-relative entropy of coherence under mutually unbiased equiangular tight frames
• Constructions of complex equiangular lines from mutually unbiased bases
• All classes of informationally complete symmetric measurements in finite dimensions