### Abstract

Determining the ultimate classical information carrying capacity of electromagnetic waves requires quantummechanical analysis to properly account for the bosonic nature of these waves. Recent work has established capacity theorems for bosonic single-user and broadcast channels, under the presumption of two minimum output entropy conjectures. Despite considerable accumulated evidence that supports the validity of these conjectures, they have yet to be proven. In this paper, it is shown that the second conjecture suffices to prove the classical capacity of the bosonic wiretap channel, which in turn would also prove the quantum capacity of the lossy bosonic channel. The preceding minimum output entropy conjectures are then shown to be simple consequences of an Entropy Photon-Number Inequality (EPnI), which is a conjectured quantum-mechanical analog of the Entropy Power Inequality (EPI) from classical information theory.

Original language | English (US) |
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Title of host publication | Proceedings - 2008 IEEE International Symposium on Information Theory, ISIT 2008 |

Pages | 91-95 |

Number of pages | 5 |

DOIs | |

State | Published - Sep 29 2008 |

Externally published | Yes |

Event | 2008 IEEE International Symposium on Information Theory, ISIT 2008 - Toronto, ON, Canada Duration: Jul 6 2008 → Jul 11 2008 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
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ISSN (Print) | 2157-8101 |

### Other

Other | 2008 IEEE International Symposium on Information Theory, ISIT 2008 |
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Country | Canada |

City | Toronto, ON |

Period | 7/6/08 → 7/11/08 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Information Systems
- Modeling and Simulation
- Applied Mathematics

### Cite this

*Proceedings - 2008 IEEE International Symposium on Information Theory, ISIT 2008*(pp. 91-95). [4594954] (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2008.4594954

**Capacity of the bosonic wiretap channel and the Entropy Photon-Number Inequality.** / Guha, Saikat; Shapiro, Jeffrey H.; Erkmen, Baris I.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings - 2008 IEEE International Symposium on Information Theory, ISIT 2008.*, 4594954, IEEE International Symposium on Information Theory - Proceedings, pp. 91-95, 2008 IEEE International Symposium on Information Theory, ISIT 2008, Toronto, ON, Canada, 7/6/08. https://doi.org/10.1109/ISIT.2008.4594954

}

TY - GEN

T1 - Capacity of the bosonic wiretap channel and the Entropy Photon-Number Inequality

AU - Guha, Saikat

AU - Shapiro, Jeffrey H.

AU - Erkmen, Baris I.

PY - 2008/9/29

Y1 - 2008/9/29

N2 - Determining the ultimate classical information carrying capacity of electromagnetic waves requires quantummechanical analysis to properly account for the bosonic nature of these waves. Recent work has established capacity theorems for bosonic single-user and broadcast channels, under the presumption of two minimum output entropy conjectures. Despite considerable accumulated evidence that supports the validity of these conjectures, they have yet to be proven. In this paper, it is shown that the second conjecture suffices to prove the classical capacity of the bosonic wiretap channel, which in turn would also prove the quantum capacity of the lossy bosonic channel. The preceding minimum output entropy conjectures are then shown to be simple consequences of an Entropy Photon-Number Inequality (EPnI), which is a conjectured quantum-mechanical analog of the Entropy Power Inequality (EPI) from classical information theory.

AB - Determining the ultimate classical information carrying capacity of electromagnetic waves requires quantummechanical analysis to properly account for the bosonic nature of these waves. Recent work has established capacity theorems for bosonic single-user and broadcast channels, under the presumption of two minimum output entropy conjectures. Despite considerable accumulated evidence that supports the validity of these conjectures, they have yet to be proven. In this paper, it is shown that the second conjecture suffices to prove the classical capacity of the bosonic wiretap channel, which in turn would also prove the quantum capacity of the lossy bosonic channel. The preceding minimum output entropy conjectures are then shown to be simple consequences of an Entropy Photon-Number Inequality (EPnI), which is a conjectured quantum-mechanical analog of the Entropy Power Inequality (EPI) from classical information theory.

UR - http://www.scopus.com/inward/record.url?scp=52349085683&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=52349085683&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2008.4594954

DO - 10.1109/ISIT.2008.4594954

M3 - Conference contribution

AN - SCOPUS:52349085683

SN - 9781424422579

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 91

EP - 95

BT - Proceedings - 2008 IEEE International Symposium on Information Theory, ISIT 2008

ER -