Informational power of the Hoggar SIC-POVM

TL;DR

This paper calculates the informational power of the Hoggar SIC-POVM in dimension 8, revealing that the most informative ensemble is a conjugate twin of the original measurement, thus advancing understanding of quantum measurement capacities.

Contribution

It provides the first explicit computation of the Hoggar SIC-POVM's informational power and identifies the maximally informative ensemble as a conjugate twin measurement.

Findings

The informational power of the Hoggar SIC-POVM in dimension 8 is explicitly computed.

The maximally informative ensemble is a conjugate twin of the original Hoggar SIC-POVM.

This work advances understanding of quantum measurement capacities in higher dimensions.

Abstract

We compute the informational power for the Hoggar SIC-POVM in dimension 8, i.e. the classical capacity of a quantum-classical channel generated by this measurement. We show that the states constituting a maximally informative ensemble form a twin Hoggar SIC-POVM being the image of the original one under a conjugation.