Fundamental Limits of Quantum-Secure Covert Communication over Bosonic Channels

Michael S. Bullock, Christos N. Gagatsos, Saikat Guha, Boulat A. Bash

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


We investigate the fundamental limit of quantum-secure covert communication over the lossy thermal noise bosonic channel, the quantum-mechanical model underlying many practical channels. We assume that the adversary has unlimited quantum information processing capabilities as well as access to all transmitted photons that do not reach the legitimate receiver. Given existence of noise that is uncontrolled by the adversary, the square root law (SRL) governs covert communication: Up to c&sqrt;n covert bits can be transmitted reliably in n channel uses. Attempting to surpass this limit results in detection with unity probability as n → &inf;. Here we present the expression for c, characterizing the SRL for the bosonic channel. We also prove that discrete-valued coherent state quadrature phase shift keying (QPSK) constellation achieves the optimal c, which is the same as that achieved by a circularly-symmetric complex-valued Gaussian prior on coherent state amplitude. Finally, while binary phase shift keying (BPSK) achieves the Holevo capacity for non-covert bosonic channels in the low received signal-to-noise ratio regime, we show that it is strictly sub-optimal for covert communication.

Original languageEnglish (US)
Article number8976410
Pages (from-to)471-482
Number of pages12
JournalIEEE Journal on Selected Areas in Communications
Issue number3
StatePublished - Mar 2020


  • Quantum cryptography
  • communication system security
  • covert communication
  • low probability of detection
  • low probability of intercept

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Electrical and Electronic Engineering


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