Working Paper Article Version 1 This version is not peer-reviewed

# Informationally Complete Characters for Quark and Lepton Mixings

Version 1 : Received: 18 May 2020 / Approved: 19 May 2020 / Online: 19 May 2020 (04:25:02 CEST)

A peer-reviewed article of this Preprint also exists.

Planat, M.; Aschheim, R.; M. Amaral, M.; Irwin, K. Informationally Complete Characters for Quark and Lepton Mixings. Symmetry 2020, 12, 1000. Planat, M.; Aschheim, R.; M. Amaral, M.; Irwin, K. Informationally Complete Characters for Quark and Lepton Mixings. Symmetry 2020, 12, 1000.

Journal reference: Symmetry 2020, 12, 1000
DOI: 10.3390/sym12061000

## Abstract

A popular account of the mixing patterns for the three generations of quarks and leptons is through the characters $\kappa$ of a finite group $G$. Here we introduce a $d$-dimensional Hilbert space with $d=cc(G)$, the number of conjugacy classes of $G$. Groups under consideration should follow two rules, (a) the character table contains both two- and three-dimensional representations with at least one of them faithful and (b) there are minimal informationally complete measurements under the action of a $d$-dimensional Pauli group over the characters of these representations. Groups with small $d$ that satisfy these rules coincide in a large part with viable ones derived so far for reproducing simultaneously the CKM (quark) and PNMS (lepton) mixing matrices. Groups leading to physical $CP$ violation are singled out.

## Subject Areas

informationally complete characters; quark and lepton mixings; CP violation; Pauli groups

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