The spin density matrix of top quark pairs produced in electron-positron annihilation including QCD radiative corrections

We calculate the spin density matrix of top quark pairs for the reaction $e^{+}{e}^{-}\to t\bar{t}X$ to order ${\alpha }_s$. As an application we show next-to-leading order results for a variety of spin observables for the $t\bar{t}$ system. These include the top quark and antiquark polarizations and $t\bar{t}$ spin-spin correlations as a function of the center-of-mass energy and of the top quark scattering angle for arbitrary longitudinal polarization of the electron/positron beam.