### Abstract

We demonstrate the achievability of a square root limit on the amount of information transmitted reliably and with low probability of detection (LPD) over the single-mode lossy bosonic channel if either the eavesdropper's measurements or the channel itself is subject to the slightest amount of excess noise. Specifically, Alice can transmit O(√n) bits to Bob over n channel uses such that Bob's average codeword error probability is upper-bounded by an arbitrarily small δ > 0 while a passive eavesdropper, Warden Willie, who is assumed to be able to collect all the transmitted photons that do not reach Bob, has an average probability of detection error that is lower-bounded by 1/2 - ε for an arbitrarily small ε > 0. We analyze the thermal noise and pure loss channels. The square root law holds for the thermal noise channel even if Willie employs a quantum-optimal measurement, while Bob is equipped with a standard coherent detection receiver. We also show that LPD communication is not possible with coherent state transmission on the pure loss channel. However, this result assumes Willie to possess an ideal receiver that is not subject to excess noise. If Willie is restricted to a practical receiver with a non-zero dark current, the square root law is achievable on the pure loss channel.

Original language | English (US) |
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Title of host publication | 2013 IEEE International Symposium on Information Theory, ISIT 2013 |

Pages | 1715-1719 |

Number of pages | 5 |

DOIs | |

State | Published - Dec 19 2013 |

Externally published | Yes |

Event | 2013 IEEE International Symposium on Information Theory, ISIT 2013 - Istanbul, Turkey Duration: Jul 7 2013 → Jul 12 2013 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
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ISSN (Print) | 2157-8095 |

### Other

Other | 2013 IEEE International Symposium on Information Theory, ISIT 2013 |
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Country | Turkey |

City | Istanbul |

Period | 7/7/13 → 7/12/13 |

### ASJC Scopus subject areas

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

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## Cite this

*2013 IEEE International Symposium on Information Theory, ISIT 2013*(pp. 1715-1719). [6620520] (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2013.6620520