The fundamental information-theoretic limits of covert, or low probability of detection/intercept (LPD/LPI), communication have been extensively studied for over a decade, resulting in thesquare root law(SRL): onlyL√ncovert bits can be reliably transmitted over time-bandwidth productn, for constantL> 0. Transmitting more either results in detection or decoding errors. The SRL imposes significant constraints on the hardware realization of mathematically guaranteed covert communication. These preclude the use of standard link maintenance operations that are taken for granted in non-covert communication. Thus, experimental validation of covert communication is under-explored: to date, only two experimental studies of SRL-based covert communication are available, both focusing on optical channels. Here, we demonstrate provably secure covert radio-frequency (RF) communication using software-defined radios (SDRs). We combine system design, theory, and experiments by 1) developing a sparse-signaling pulse shape to enable covert transmission of data in an environment with potential mobility, 2) proving the covertness of the resulting system, and 3) validating the theoretical predictions by implementing it on SDRs. We uncover and address unique challenges specific to using SDR architecture for covert communications. This opens practical avenues for implementing covert communication systems and raises further research questions.

We explore covert communication of qubits over an arbitrary quantum channel. Covert communication conceals the transmissions in the channel noise, ensuring that an adversary is unable to detect their presence. We show the achievability of a square root law (SRL) for quantum covert communication similar to that for classical:$M(n) \sqrt{n}$qubits can be transmitted covertly and reliably over$n$uses of a general quantum channel. We lower bound$M (n)$with and without assistance from a two-way covert classical channel. In the former case, we quantify the number of classical covert bits sufficient for our protocol.

We investigate covert communication over general memoryless classical-quantum channels with fixed finite-size input alphabets. We show that the square root law (SRL) governs covert communication in this setting when product a ofninput states is used:$L_{\mathrm { SRL}}\sqrt {n}+o(\sqrt {n})$covert bits (but no more) can be reliably transmitted innuses of classical-quantum channel, where$L_{\mathrm { SRL}}\gt 0$is a channel-dependent constant that we callcovert capacity. We also show that ensuring covertness requires$J_{\mathrm { SRL}}\sqrt {n}+o(\sqrt {n})$bits secret key shared by the communicating parties prior to transmission, where$J_{\mathrm { SRL}}\geq 0$is a channel-dependent constant. We assume a quantum-powerful adversary that can perform an arbitrary joint (entangling) measurement on allnchannel uses. We determine the single-letter expressions for$L_{\mathrm { SRL}}$and$J_{\mathrm { SRL}}$, and establish conditions when$J_{\mathrm { SRL}}=0$(i.e., no pre-shared secret key is needed). Finally, we evaluate scenarios where covert communication is not governed by the SRL.

We study quantum-secure covert-communication over lossy thermal-noise bosonic channels, the quantum mechanical model for many practical channels. We derive the expressions for the covert capacity of these channels: Lno-EA, when Alice and Bob share only a classical secret, and LEA, when they benefit from entanglement assistance. Entanglement assistance alters the fundamental scaling law for covert communication. Instead of Lno-EA√n-rno-EA(n), rno-EA(n) = o(√n), entanglement assistance allows LEA√n log n - rEA(n), rEA(n) = o(√n log n), covert bits to be transmitted reliably over n channel uses. However, noise in entanglement storage erases the log n gain from our achievability; work on the matching converse is ongoing.