Uncertainty and certainty relations for the Pauli observables in terms of the Rényi entropies of order α∈(0;1]
We obtain uncertainty and certainty relations of state-independent form for the three Pauli observables with use of the Rényi entropies of order α ∈ (0; 1]. It is shown that these entropic bounds are tight in the sense that they are always reached with certain pure states. A new result is the condition for equality in Rényi-entropy uncertainty relations for the Pauli observables. Upper entropic bounds in the pure-state case are also novel. Combining the presented bounds leads to a band, in which the rescaled average Rényi α-entropy ranges for a pure measured state. A width of this band is compared with the Tsallis formulation derived previously.