Abstract :
[en] Among all possible spin states, spin-coherent states are the most classical because the spin expectation value in these states yields a vector of maximal norm pointing in a well defined direction. In contrast, anticoherent spin state to order t are such that <(J.n)^k> is independent of the unit vector n for k = 1, ..., t [1]. By construction, coherent and anticoherent spin states are at both ends of the spectrum of classicality. The aim of this work is to position all possible spin states on such a spectrum, that is to provide measures of anticoherence. To this aim, we introduce an axiomatic definition of anticoherence measures to any order t. In particular, we show that the total variance of a pure spin state, first introduced in [2] can be used to define a measure of anticoherence to order 1. We describe a systematic way of constructing anticoherence measures to any order that relies on the mapping between spin-j states and symmetric states of N = 2j spin-1/2. In particular, we exploit the fact that anticoherent spin states to order t have maximally mixed t-spin-1/2 reduced density matrices in the symmetric subspace [3].
[1] J. Zimba, Electron. J. Theor. Phys. 3, 143 (2006).
[2] A. A. Klyachko, B. Öztop, and A. S. Shumovsky, Phys. Rev. A 75, 032315 (2007).
[3] D. Baguette, T. Bastin, and J. Martin, Phys. Rev A 90, 032314 (2014).
