Classical and quantum correlations in an ideal gas of particles obeying fractional exclusion statistics

We study the correlations in a two component gas of non-interacting particles obeying fractional exclusion statistics characterized by a parameter α ∈ [0, 1] that interpolates between bosonic (α = 0) and fermionic (α = 1) statistics. We discuss the behaviour of the total correlations, entanglement, classical correlations and quantum discord in the two spin density matrix (‘spin’ here refers to the two internal degrees of freedom) as a function of the statistical parameter α and the relative distance between the two spins. We show that the spins are entangled only for statistics α > α∗ = 2/3 (independent of the number of spatial dimensions) and provided that the relative distance between the spins is less than a certain critical value re which depends on the Fermi wave number and the statistics parameter. However, the quantum discord is non-vanishing even in the absence of entanglement, vanishing (for zero temperature) only in the limit of very large relative separations, i.e., at distances where quantum statistics play no role.