# Secure coherent-state quantum key distribution protocols with efficient reconciliation

## Abstract

We study the equivalence of a realistic quantum key distribution protocol using coherent states and homodyne detection with a formal entanglement purification protocol. Maximally entangled qubit pairs that one can extract in the formal protocol correspond to secret key bits in the realistic protocol. More specifically, we define a qubit encoding scheme that allows the formal protocol to produce more than one entangled qubit pair per entangled oscillator pair or, equivalently for the realistic protocol, more than one secret key bit per coherent state. The entanglement parameters are estimated using quantum tomography. We analyze the properties of the encoding scheme and investigate the resulting secret key rate in the important case of the attenuation channel.

- Authors:

- QuIC, Ecole Polytechnique, Universite Libre de Bruxelles, CP 165/59, 1050 Brussels (Belgium)
- (Switzerland)

- Publication Date:

- OSTI Identifier:
- 20717715

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 71; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevA.71.052304; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; ANNIHILATION OPERATORS; ATTENUATION; DETECTION; DISTRIBUTION; EIGENSTATES; INFORMATION THEORY; OSCILLATORS; QUANTUM COMPUTERS; QUANTUM CRYPTOGRAPHY; QUANTUM ENTANGLEMENT; QUBITS; TOMOGRAPHY

### Citation Formats

```
Assche, G. van, Cerf, N.J., Iblisdir, S., and GAP-Optique, University of Geneva, 20 rue de l'Ecole-de-Medecine, CH-1211 Geneva.
```*Secure coherent-state quantum key distribution protocols with efficient reconciliation*. United States: N. p., 2005.
Web. doi:10.1103/PhysRevA.71.052304.

```
Assche, G. van, Cerf, N.J., Iblisdir, S., & GAP-Optique, University of Geneva, 20 rue de l'Ecole-de-Medecine, CH-1211 Geneva.
```*Secure coherent-state quantum key distribution protocols with efficient reconciliation*. United States. doi:10.1103/PhysRevA.71.052304.

```
Assche, G. van, Cerf, N.J., Iblisdir, S., and GAP-Optique, University of Geneva, 20 rue de l'Ecole-de-Medecine, CH-1211 Geneva. Sun .
"Secure coherent-state quantum key distribution protocols with efficient reconciliation". United States. doi:10.1103/PhysRevA.71.052304.
```

```
@article{osti_20717715,
```

title = {Secure coherent-state quantum key distribution protocols with efficient reconciliation},

author = {Assche, G. van and Cerf, N.J. and Iblisdir, S. and GAP-Optique, University of Geneva, 20 rue de l'Ecole-de-Medecine, CH-1211 Geneva},

abstractNote = {We study the equivalence of a realistic quantum key distribution protocol using coherent states and homodyne detection with a formal entanglement purification protocol. Maximally entangled qubit pairs that one can extract in the formal protocol correspond to secret key bits in the realistic protocol. More specifically, we define a qubit encoding scheme that allows the formal protocol to produce more than one entangled qubit pair per entangled oscillator pair or, equivalently for the realistic protocol, more than one secret key bit per coherent state. The entanglement parameters are estimated using quantum tomography. We analyze the properties of the encoding scheme and investigate the resulting secret key rate in the important case of the attenuation channel.},

doi = {10.1103/PhysRevA.71.052304},

journal = {Physical Review. A},

number = 5,

volume = 71,

place = {United States},

year = {Sun May 15 00:00:00 EDT 2005},

month = {Sun May 15 00:00:00 EDT 2005}

}