# Renyi Entropy and the Uncertainty Relations

## Abstract

Quantum mechanical uncertainty relations for the position and the momentum and for the angle and the angular momentum are expressed in the form of inequalities involving the Renyi entropies. These uncertainty relations hold not only for pure but also for mixed states. Analogous uncertainty relations are valid also for a pair of complementary observables (the analogs of x and p) in N-level systems. All these uncertainty relations become more attractive when expressed in terms of the symmetrized Renyi entropies. The mathematical proofs of all the inequalities discussed in this paper can be found in Phys. Rev. A 74, No. 5 (2006); arXiv:quant-ph/0608116.

- Authors:

- Center for Theoretical Physics, Al. Lotnikow 32/46, 02-668 Warsaw (Poland)

- Publication Date:

- OSTI Identifier:
- 21054921

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: AIP Conference Proceedings; Journal Volume: 889; Journal Issue: 1; Conference: 4. international conference on foundations of probability and physics, Vaexjoe (Sweden), 4-9 Jun 2006; Other Information: DOI: 10.1063/1.2713446; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANGULAR MOMENTUM; ENERGY LEVELS; ENTROPY; MIXED STATE; QUANTUM MECHANICS; UNCERTAINTY PRINCIPLE

### Citation Formats

```
Bialynicki-Birula, Iwo.
```*Renyi Entropy and the Uncertainty Relations*. United States: N. p., 2007.
Web. doi:10.1063/1.2713446.

```
Bialynicki-Birula, Iwo.
```*Renyi Entropy and the Uncertainty Relations*. United States. doi:10.1063/1.2713446.

```
Bialynicki-Birula, Iwo. Wed .
"Renyi Entropy and the Uncertainty Relations". United States.
doi:10.1063/1.2713446.
```

```
@article{osti_21054921,
```

title = {Renyi Entropy and the Uncertainty Relations},

author = {Bialynicki-Birula, Iwo},

abstractNote = {Quantum mechanical uncertainty relations for the position and the momentum and for the angle and the angular momentum are expressed in the form of inequalities involving the Renyi entropies. These uncertainty relations hold not only for pure but also for mixed states. Analogous uncertainty relations are valid also for a pair of complementary observables (the analogs of x and p) in N-level systems. All these uncertainty relations become more attractive when expressed in terms of the symmetrized Renyi entropies. The mathematical proofs of all the inequalities discussed in this paper can be found in Phys. Rev. A 74, No. 5 (2006); arXiv:quant-ph/0608116.},

doi = {10.1063/1.2713446},

journal = {AIP Conference Proceedings},

number = 1,

volume = 889,

place = {United States},

year = {Wed Feb 21 00:00:00 EST 2007},

month = {Wed Feb 21 00:00:00 EST 2007}

}

DOI: 10.1063/1.2713446

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