Anticoherent Subspaces

TL;DR

This paper introduces the concept of anticoherent subspaces in quantum spin systems, providing new constructions using invariant polynomial algebras and linking their existence to higher-rank numerical ranges and spherical designs.

Contribution

It extends anticoherent states to subspaces, offers novel construction methods, and connects these to algebraic and geometric properties of spin states.

Findings

Constructed anticoherent subspaces using invariant polynomial algebras.

Linked anticoherent subspaces to higher-rank numerical ranges.

Showed that vectors in these subspaces have Majorana representations as spherical designs.

Abstract

We extend the notion of anticoherent spin states to anticoherent subspaces. An anticoherent subspace of order t, is a subspace whose unit vectors are all anticoherent states of order t. We use Klein's description of algebras of polynomials which are invariant under finite subgroups of SU(2) to provide constructions of anticoherent subspaces. Furthermore, we show a connection between the existence of these subspaces and the properties of the higher-rank numerical range for a set of spin observables. We also note that these constructions give us subspaces of spin states all of whose unit vectors have Majorana representations which are spherical designs of order at least t.