Anticoherence measures for pure spin states

TL;DR

This paper introduces measures to quantify the degree of anticoherence in pure spin states, using higher order moments and Majorana representation, to better understand their coherence properties.

Contribution

The paper develops systematic anticoherence measures for pure spin states of any order based on moments and Majorana representation, connecting them with quantum coherence measures.

Findings

Anticoherence measures effectively quantify anticoherence levels.

Most spin states are neither coherent nor anticoherent but can be close to either.

The measures help investigate existence of anticoherent states with degenerated Majorana points.

Abstract

The set of pure spin states with vanishing spin expectation value can be regarded as the set of the less coherent pure spin states. This set can be divided into a finite number of nested subsets on the basis of higher order moments of the spin operators. This subdivision relies on the notion of anticoherent spin state to order $t$: A spin state is said to be anticoherent to order $t$ if the moment of order $k$ of the spin components along any directions are equal for $k= 1, 2,\ldots, t$. Most spin states are neither coherent nor anticoherent, but can be arbitrary close to one or the other. In order to quantify the degree of anticoherence of pure spin states, we introduce the notion of anticoherence measures. By relying on the mapping between spin-$j$ states and symmetric states of $2j$ spin-$1/2$ (Majorana representation), we present a systematic way of constructing anticoherence measures to any order. We briefly discuss their connection with measures of quantum coherence. Finally, we illustrate our measures on various spin states and use them to investigate the problem of the existence of anticoherent spin states with degenerated Majorana points.