Abstract

In this paper, we present some new properties of fiducial states in prime dimensions. We parameterize fiducial operators on eigenvectors bases of displacement operators, which allows us to find a manifold Omega of Hermitian operators satisfying Tr(rho) = Tr(rho(2)) = 1 for any rho in Omega. This manifold contains the complete set of fiducial pure states in every prime dimension. Indeed, any quantum state rho >= 0 belonging to Omega is a fiducial pure state. Also, we present an upper bound for every probability associated with the mutually unbiased decomposition of fiducial states. This bound allows us to prove that every fiducial state tends to be mutually unbiased to the maximal set of mutually unbiased bases in higher prime dimensions. Finally, we show that any rho in Omega minimizes an entropic uncertainty principle related to the second-order Renyi entropy.