Orthonormal bases of extreme quantumness

TL;DR

This paper introduces a measure of quantumness for orthonormal bases of spin states, identifying those with extreme quantum properties and exploring their symmetries and entanglement characteristics.

Contribution

It proposes a new quantumness measure based on anticoherence and Wehrl entropy, revealing bases with maximal quantum features and their geometric symmetries.

Findings

Identified bases with extreme quantumness and symmetry properties.

Connected maximally entangled bases to the symmetric subspace of multipartite systems.

Discovered iso-coherent bases with uniform spin-coherence levels.

Abstract

Spin anticoherent states acquired recently a lot of attention as the most "quantum" states. Some coherent and anticoherent spin states are known as optimal quantum rotosensors. In this work, we introduce a measure of quantumness for orthonormal bases of spin states, determined by the average anticoherence of individual vectors and the Wehrl entropy. In this way, we identify the most coherent and most quantum states, which lead to orthogonal measurements of extreme quantumness. Their symmetries can be revealed using the Majorana stellar representation, which provides an intuitive geometrical representation of a pure state by points on a sphere. Results obtained lead to maximally (minimally) entangled bases in the $2j+1$ dimensional symmetric subspace of the $2^{2j}$ dimensional space of states of multipartite systems composed of $2j$ qubits. Some bases found are iso-coherent as they consist of all states of the same degree of spin-coherence.