Computational encryption, information-theoretic secrecy and quantum cryptography offer progressively stronger security against unauthorized decoding of messages contained in communication transmissions. However, these approaches do not ensure stealth—that the mere presence of message-bearing transmissions be undetectable. We characterize the ultimate limit of how much data can be reliably and covertly communicated over the lossy thermal-noise bosonic channel (which models various practical communication channels). We show that whenever there is some channel noise that cannot in principle be controlled by an otherwise arbitrarily powerful adversary—for example, thermal noise from blackbody radiation—the number of reliably transmissible covert bits is at most proportional to the square root of the number of orthogonal modes (the time-bandwidth product) available in the transmission interval. We demonstrate this in a proof-of-principle experiment. Our result paves the way to realizing communications that are kept covert from an all-powerful quantum adversary.
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