# Magic informationally complete POVMs with permutations

## TL;DR

This paper introduces a class of informationally complete POVMs derived from magic states associated with permutation gates, revealing geometric structures and contextuality in quantum systems of dimensions 2 to 12.

## Contribution

It demonstrates that certain magic states linked to permutation gates generate asymmetric IC-POVMs with geometric and contextuality properties across multiple dimensions.

## Key findings

- IC-POVMs exhibit simple finite geometries.
- Dimensions 4, 8, and 9 relate to multi-qubit and multi-qutrit contextuality.
- Dimensions 2 to 12 analyzed for geometric structures.

## Abstract

Eigenstates of permutation gates are either stabilizer states (for gates in the Pauli group) or magic states, thus allowing universal quantum computation [M. Planat and Rukhsan-Ul-Haq, Preprint 1701.06443]. We show in this paper that a subset of such magic states, when acting on the generalized Pauli group, define (asymmetric) informationally complete POVMs. Such IC-POVMs, investigated in dimensions $2$ to $12$, exhibit simple finite geometries in their projector products and, for dimensions $4$ and $8$ and $9$, relate to two-qubit, three-qubit and two-qutrit contextuality.