Uncertainties of the standard quantum teleportation channel

From the perspective of state-channel interaction, standard quantum teleportation can be viewed as a communication process characterized by both input and output, functioning as a quantum depolarizing channel. To achieve a precise quantification of the quantumness introduced by this channel, we examine its uncertainties, which encompass both state-dependent and state-independent uncertainties. Specifically, for qudit systems, we provide general formulas for these uncertainties. We analyze the uncertainties associated with standard quantum teleportation when induced by isotropic states, Werner states, and X-states, and we elucidate the correlation between these uncertainties and the parameters of the specific mixed states. Our findings demonstrate the validity of quantifying these uncertainties.