# Optimal multicopy asymmetric Gaussian cloning of coherent states

## Abstract

We investigate the asymmetric Gaussian cloning of coherent states which produces M copies from N input replicas in such a way that the fidelity of each copy may be different. We show that the optimal asymmetric Gaussian cloning can be performed with a single phase-insensitive amplifier and an array of beam splitters. We obtain a simple analytical expression characterizing the set of optimal asymmetric Gaussian cloning machines and prove the optimality of these cloners using the formalism of Gaussian completely positive maps and semidefinite programming techniques. We also present an alternative implementation of the asymmetric cloning machine where the phase-insensitive amplifier is replaced with a beam splitter, heterodyne detector, and feedforward.

- Authors:

- Department of Optics, Palacky University, 17. listopadu 50, 77200 Olomouc (Czech Republic)
- QuIC, Ecole Polytechnique, CP 165, Universite Libre de Bruxelles, 1050 Brussels (Belgium)

- Publication Date:

- OSTI Identifier:
- 20982504

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevA.75.052335; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AMPLIFIERS; ANNIHILATION OPERATORS; ASYMMETRY; BEAM SPLITTING; COMMUNICATIONS; EIGENSTATES; GAUSSIAN PROCESSES; INFORMATION THEORY; OPTICS

### Citation Formats

```
Fiurasek, Jaromir, and Cerf, Nicolas J.
```*Optimal multicopy asymmetric Gaussian cloning of coherent states*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVA.75.052335.

```
Fiurasek, Jaromir, & Cerf, Nicolas J.
```*Optimal multicopy asymmetric Gaussian cloning of coherent states*. United States. doi:10.1103/PHYSREVA.75.052335.

```
Fiurasek, Jaromir, and Cerf, Nicolas J. Tue .
"Optimal multicopy asymmetric Gaussian cloning of coherent states". United States.
doi:10.1103/PHYSREVA.75.052335.
```

```
@article{osti_20982504,
```

title = {Optimal multicopy asymmetric Gaussian cloning of coherent states},

author = {Fiurasek, Jaromir and Cerf, Nicolas J.},

abstractNote = {We investigate the asymmetric Gaussian cloning of coherent states which produces M copies from N input replicas in such a way that the fidelity of each copy may be different. We show that the optimal asymmetric Gaussian cloning can be performed with a single phase-insensitive amplifier and an array of beam splitters. We obtain a simple analytical expression characterizing the set of optimal asymmetric Gaussian cloning machines and prove the optimality of these cloners using the formalism of Gaussian completely positive maps and semidefinite programming techniques. We also present an alternative implementation of the asymmetric cloning machine where the phase-insensitive amplifier is replaced with a beam splitter, heterodyne detector, and feedforward.},

doi = {10.1103/PHYSREVA.75.052335},

journal = {Physical Review. A},

number = 5,

volume = 75,

place = {United States},

year = {Tue May 15 00:00:00 EDT 2007},

month = {Tue May 15 00:00:00 EDT 2007}

}