Anticoherence of spin states with point group symmetries

TL;DR

This paper explores the relationship between point-group symmetries in Majorana representations of multiqubit states and their anticoherence properties, revealing new classes of highly entangled symmetric states.

Contribution

It introduces three characterizations of anticoherence linked to point-group symmetries and constructs infinite families of anticoherent states with arbitrary order.

Findings

Anticoherent states can be characterized by point-group symmetries.

Existence of anticoherent states with arbitrary order.

New classes of highly entangled symmetric states identified.

Abstract

We investigate multiqubit permutation-symmetric states with maximal entropy of entanglement. Such states can be viewed as particular spin states, namely anticoherent spin states. Using the Majorana representation of spin states in terms of points on the unit sphere, we analyze the consequences of a point-group symmetry in their arrangement on the quantum properties of the corresponding state. We focus on the identification of anticoherent states (for which all reduced density matrices in the symmetric subspace are maximally mixed) associated with point-group symmetric sets of points. We provide three different characterizations of anticoherence, and establish a link between point symmetries, anticoherence and classes of states equivalent through stochastic local operations with classical communication (SLOCC). We then investigate in detail the case of small numbers of qubits, and construct infinite families of anticoherent states with point-group symmetry of their Majorana points, showing that anticoherent states do exist to arbitrary order.