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arXiv · 1308.5051

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

Alexey E. Rastegin
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Abstract

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

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Alexey E. Rastegin. 2014-04-02. Uncertainty and certainty relations for the Pauli observables in terms of the Rényi entropies of order $α\in(0;1]$. https://doi.org/10.1088/0253-6102%2F61%2F3%2F04

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