Optimal state for keeping reference frames aligned and the Platonic solids

TL;DR

This paper identifies the most sensitive quantum states for aligning reference frames, revealing a connection to Platonic solids through the Majorana representation, and shows these states are supported on the symmetric subspace.

Contribution

It introduces the optimal N-qubit states for reference frame alignment and links them to Platonic solids via the Majorana representation.

Findings

Optimal states are supported on the symmetric subspace.

These states are mathematically equivalent to a single spin J=N/2.

A connection between optimal states and Platonic solids is established.

Abstract

The optimal N qubit states featuring highest sensitivity to small misalignment of cartesian reference frames are found using the Quantum Cramer-Rao bound. It is shown that the optimal states are supported on the symmetric subspace and hence are mathematically equivalent to a single spin J=N/2. Majorana representation of spin states is used to reveal a beautiful connection between the states optimal for aligning reference frames and the platonic solids.