# Finite key analysis for symmetric attacks in quantum key distribution

## Abstract

We introduce a constructive method to calculate the achievable secret key rate for a generic class of quantum key distribution protocols, when only a finite number n of signals is given. Our approach is applicable to all scenarios in which the quantum state shared by Alice and Bob is known. In particular, we consider the six state protocol with symmetric eavesdropping attacks, and show that for a small number of signals, i.e., below n{approx}10{sup 4}, the finite key rate differs significantly from the asymptotic value for n{yields}{infinity}. However, for larger n, a good approximation of the asymptotic value is found. We also study secret key rates for protocols using higher-dimensional quantum systems.

- Authors:

- Institut fuer Theoretische Physik III, Heinrich-Heine-Universitaet Duesseldorf, D-40225 Duesseldorf (Germany)

- Publication Date:

- OSTI Identifier:
- 20857858

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. A

- Additional Journal Information:
- Journal Volume: 74; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevA.74.042340; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; APPROXIMATIONS; DISTRIBUTION; ENERGY LEVELS; INFORMATION THEORY; QUANTUM CRYPTOGRAPHY; QUANTUM MECHANICS; QUANTUM NUMBERS; SECRECY PROTECTION; SIGNALS

### Citation Formats

```
Meyer, Tim, Kampermann, Hermann, Kleinmann, Matthias, and Bruss, Dagmar.
```*Finite key analysis for symmetric attacks in quantum key distribution*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVA.74.042340.

```
Meyer, Tim, Kampermann, Hermann, Kleinmann, Matthias, & Bruss, Dagmar.
```*Finite key analysis for symmetric attacks in quantum key distribution*. United States. doi:10.1103/PHYSREVA.74.042340.

```
Meyer, Tim, Kampermann, Hermann, Kleinmann, Matthias, and Bruss, Dagmar. Sun .
"Finite key analysis for symmetric attacks in quantum key distribution". United States. doi:10.1103/PHYSREVA.74.042340.
```

```
@article{osti_20857858,
```

title = {Finite key analysis for symmetric attacks in quantum key distribution},

author = {Meyer, Tim and Kampermann, Hermann and Kleinmann, Matthias and Bruss, Dagmar},

abstractNote = {We introduce a constructive method to calculate the achievable secret key rate for a generic class of quantum key distribution protocols, when only a finite number n of signals is given. Our approach is applicable to all scenarios in which the quantum state shared by Alice and Bob is known. In particular, we consider the six state protocol with symmetric eavesdropping attacks, and show that for a small number of signals, i.e., below n{approx}10{sup 4}, the finite key rate differs significantly from the asymptotic value for n{yields}{infinity}. However, for larger n, a good approximation of the asymptotic value is found. We also study secret key rates for protocols using higher-dimensional quantum systems.},

doi = {10.1103/PHYSREVA.74.042340},

journal = {Physical Review. A},

issn = {1050-2947},

number = 4,

volume = 74,

place = {United States},

year = {2006},

month = {10}

}

Other availability

Save to My Library

You must Sign In or Create an Account in order to save documents to your library.