How ‘hot’ are mixed quantum states?

Given a mixed quantum state ρ of a qudit, we consider any observable M as a kind of ‘thermometer’ in the following sense. Given a source which emits pure states with these or those distributions, we select such distributions that the appropriate average value of the observable M is equal to the average TrMρ of M in the stare ρ. Among those distributions we find the most typical one, namely, having the highest differential entropy. We call this distribution conditional Gibbs ensemble as it turns out to be a Gibbs distribution characterized by a temperature-like parameter β. The expressions establishing the liaisons between the density operator ρ and its temperature parameter β are provided. Within this approach, the uniform mixed state has the highest ‘temperature’, which tends to zero as the state in question approaches to a pure state.