Uncertainty and certainty relations for the Pauli observables in terms of the Rényi entropies of order $\alpha \in (0;1]$

Abstract

We obtain uncertainty and certainty relations of state-independent form for the three Pauli observables with use of the Rényi entropies of order $\alpha \in (0;1]$. 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 conditions 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 $\alpha$-entropy ranges for a pure measured state. A width of this band is compared with the Tsallis formulation derived previously.

6 pages, one figure. This version matches the journal version. arXiv admin note: text overlap with arXiv:1212.4242

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Cited by in corpus (5)

• Entropic Uncertainty Relations and their Applications
• Rényi entropy uncertainty relation for successive projective measurements
• Fine-grained uncertainty relations for several quantum measurements
• Separability conditions based on local fine-grained uncertainty relations
• Uncertainty and certainty relations for successive projective measurements of a qubit in terms of Tsallis' entropies