# On Generalized Stam Inequalities and Fisher-Rényi Complexity Measures

@article{Zozor2017OnGS, title={On Generalized Stam Inequalities and Fisher-R{\'e}nyi Complexity Measures}, author={Steeve Zozor and David Puertas-Centeno and Jes{\'u}s S. Dehesa}, journal={Entropy}, year={2017}, volume={19}, pages={493} }

Information-theoretic inequalities play a fundamental role in numerous scientific and technological areas (e.g., estimation and communication theories, signal and information processing, quantum physics,... ) as they generally express the impossibility to have a complete description of a system via a finite number of information measures. In particular, they gave rise to the design of various quantifiers (statistical complexity measures) of the internal complexity of a (quantum) system. In this…

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## References

SHOWING 1-10 OF 99 REFERENCES

### The biparametric Fisher–Rényi complexity measure and its application to the multidimensional blackbody radiation

- Computer Science
- 2017

It is shown that the biparametric Fisher–Rényi measure of this quantum system has a universal character in the sense that it does not depend on temperature nor on any physical constant, but only on the space dimensionality d.

### Entanglement Detection: Complexity and Shannon Entropic Criteria

- Computer ScienceIEEE Transactions on Information Theory
- 2013

A simple general formalism is proposed for this variant of the separability problem and shows the equivalence of many seemingly different covariance-matrix-based criteria; it offers guidance on the study of and reveals the inherent limitations of covariance and Shannon entropic criteria.

### Upper bounds on Shannon and Rényi entropies for central potentials

- Computer Science
- 2011

The Renyi and Shannon entropies are information-theoretic measures, which have enabled to formulate the position–momentum uncertainty principle in a much more adequate and stringent way than the…

### Biparametric complexities and generalized Planck radiation law

- Physics
- 2017

Complexity theory embodies some of the hardest, most fundamental and most challenging open problems in modern science. The very term complexity is very elusive, so the main goal of this theory is to…

### On a (β,q)-generalized Fisher information and inequalities involving q-Gaussian distributions

- Mathematics, Computer ScienceArXiv
- 2012

It is shown that the minimization of the generalized Fisher information also leads a generalized q-Gaussian, and an extended Stam inequality is given that links the generalized entropies, the generalized Fischer information, and a elliptic moment.

### General entropy-like uncertainty relations in finite dimensions

- Computer Science
- 2014

A nontrivial lower bound is obtained for the sum of generalized entropies for any pair of entropic functionals, which is valid for both pure and mixed states and is inspired by that of de Vicente and S?nchez-Ruiz.

### Upper bounds on quantum uncertainty products and complexity measures

- Computer Science
- 2011

The position-momentum Shannon and Renyi uncertainty products of general quantum systems are shown to be bounded not only from below (through the known uncertainty relations), but also from above in…

### Statistical Complexity and Fisher-Shannon Information. Applications

- Computer ScienceArXiv
- 2012

A statistical measure of complexity and the Fisher-Shannon information product are introduced and their properties are discussed and different applications in discrete and continuous systems are shown.

### Information theory of D-dimensional hydrogenic systems: Application to circular and Rydberg states

- Physics
- 2010

The analytic information theory of quantum systems includes the exact determination of their spatial extension or multidimensional spreading in both position and momentum spaces by means of the…