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Entropic uncertainty relations for general symmetric informationally complete positive operator-valued measures and mutually unbiased measurements

Shan Huang, Zeng‐Bing Chen, Shengjun Wu

We construct inequalities between R\'enyi $\ensuremath{\alpha}$-entropy and the indexes of coincidence of probability distributions, based on which we obtain improved state-dependent entropic uncertainty relations for general symmetric informationally complete positive operator-valued measures (SIC-POVMs) and mutually unbiased measurements (MUMs). We show that our uncertainty relations for general SIC-POVMs and MUMs can be tight for sufficiently mixed states, and, moreover, comparisons to the numerically optimal results are made via information diagrams.We construct inequalities between R\'enyi $\ensuremath{\alpha}$-entropy and the indexes of coincidence of probability distributions, based on which we obtain improved state-dependent entropic uncertainty relations for general symmetric informationally complete positive operator-valued measures (SIC-POVMs) and mutually unbiased measurements (MUMs). We show that our uncertainty relations for general SIC-POVMs and MUMs can be tight for sufficiently mixed states, and, moreover, comparisons to the numerically optimal results are made via information diagrams.

arXiv:2011.00808Physical Review AApr 6, 202110 citations

Constructing symmetric informationally complete positive-operator-valued measures in Bloch space

Roberto Salazar, Dardo Goyeneche, A. Delgado +1 more

Physics Letters ADec 13, 20118 citations

Symmetric informationally complete positive operator valued measure and probability representation of quantum mechanics

Sergey N. Filippov, Vladimir I. Man’ko

arXiv:1005.4091Journal of Russian Laser ResearchMay 1, 201030 citations

Operational link between mutually unbiased bases and symmetric informationally complete positive operator-valued measures

Roberto Beneduci, Tom Bullock, Paul Busch +3 more

We exhibit an operational connection between mutually unbiased bases and symmetric informationally complete positive operator-valued measures. Assuming that the latter exists, we show that there is a strong link between these two structures in all prime power dimensions. We also demonstrate that a similar link cannot exist in dimension 6.

arXiv:1306.6002Physical Review ASep 13, 201324 citations

All classes of informationally complete symmetric measurements in finite dimensions

Katarzyna Siudzińska

A broad class of informationally complete symmetric measurements is introduced. It can be understood as a common generalization of symmetric, informationally complete positive operator-valued measures and mutually unbiased bases. Additionally, it provides a natural way to define two more families of mutually unbiased symmetric measurement operators in any finite dimension. We show a general method of their construction, together with an example of an optimal measurement. Finally, we analyze the properties of symmetric measurements and provide applications in entropic relations and entanglement detection.A broad class of informationally complete symmetric measurements is introduced. It can be understood as a common generalization of symmetric, informationally complete positive operator-valued measures and mutually unbiased bases. Additionally, it provides a natural way to define two more families of mutually unbiased symmetric measurement operators in any finite dimension. We show a general method of their construction, together with an example of an optimal measurement. Finally, we analyze the properties of symmetric measurements and provide applications in entropic relations and entanglement detection.

arXiv:2111.08101Physical Review AApr 12, 202247 citations

Mathematical structure of positive operator valued measures and applications

Roberto Beneduci

Nov 17, 20143 citations

Structural Relations Between General Symmetric Informationally Complete Positive Operator-valued Measures and Mutually Unbiased Measurements

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