# Quantum key distribution with finite resources: Secret key rates via Renyi entropies

## Abstract

A realistic quantum key distribution (QKD) protocol necessarily deals with finite resources, such as the number of signals exchanged by the two parties. We derive a bound on the secret key rate which is expressed as an optimization problem over Renyi entropies. Under the assumption of collective attacks by an eavesdropper, a computable estimate of our bound for the six-state protocol is provided. This bound leads to improved key rates in comparison to previous results.

- Authors:

- Institute for Theoretical Physics III, Heinrich-Heine-universitaet Duesseldorf, D-40225 Duesseldorf (Germany)

- Publication Date:

- OSTI Identifier:
- 22068666

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. A

- Additional Journal Information:
- Journal Volume: 84; Journal Issue: 3; Other Information: (c) 2011 American Institute of Physics; Country of input: Syrian Arab Republic; Journal ID: ISSN 1050-2947

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 74 ATOMIC AND MOLECULAR PHYSICS; DISTRIBUTION; ENTROPY; OPTIMIZATION; QUANTUM MECHANICS; SIGNALS

### Citation Formats

```
Abruzzo, Silvestre, Kampermann, Hermann, Mertz, Markus, and Bruss, Dagmar.
```*Quantum key distribution with finite resources: Secret key rates via Renyi entropies*. United States: N. p., 2011.
Web. doi:10.1103/PHYSREVA.84.032321.

```
Abruzzo, Silvestre, Kampermann, Hermann, Mertz, Markus, & Bruss, Dagmar.
```*Quantum key distribution with finite resources: Secret key rates via Renyi entropies*. United States. doi:10.1103/PHYSREVA.84.032321.

```
Abruzzo, Silvestre, Kampermann, Hermann, Mertz, Markus, and Bruss, Dagmar. Thu .
"Quantum key distribution with finite resources: Secret key rates via Renyi entropies". United States. doi:10.1103/PHYSREVA.84.032321.
```

```
@article{osti_22068666,
```

title = {Quantum key distribution with finite resources: Secret key rates via Renyi entropies},

author = {Abruzzo, Silvestre and Kampermann, Hermann and Mertz, Markus and Bruss, Dagmar},

abstractNote = {A realistic quantum key distribution (QKD) protocol necessarily deals with finite resources, such as the number of signals exchanged by the two parties. We derive a bound on the secret key rate which is expressed as an optimization problem over Renyi entropies. Under the assumption of collective attacks by an eavesdropper, a computable estimate of our bound for the six-state protocol is provided. This bound leads to improved key rates in comparison to previous results.},

doi = {10.1103/PHYSREVA.84.032321},

journal = {Physical Review. A},

issn = {1050-2947},

number = 3,

volume = 84,

place = {United States},

year = {2011},

month = {9}

}

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