The standard security approach in communications aims to prevent a malicious eavesdropper from retrieving the information that is transmitted to the legitimate receiver.

However, privacy and safety concerns may require an even stronger security criterion. In covert communication, not only the information is kept secret, but the transmission itself must be concealed from detection by an adversary.

Despite the severity of such limitations, it is possible to communicate O(√n) bits of information in a block of n transmissions via a noisy channel, in all but trivial scenarios.

That is, the sender (Alice) can use an error-correction code to map O(√n) information bits into codewords of length n, such that the legitimate receiver (Bob) can decode the information reliably, while the adversary (Willie) cannot detect the transmission. Previously, it was shown that pre-shared entanglement can improve the scaling to O(√n log⁡n ) information bits in the continuousvariable setting, for Gaussian bosonic channels (Gagatsos et al., 2020).

In some information-theoretic frameworks, coding scales are larger in continuous-variable models, compared to the discrete-variable setting. Therefore, until now, it was not clear whether the logarithmic factor can be achieved in discrete-variable covert communication. Here, we study covert communication via the qubit depolarizing channel with entanglement assistance, in different scenarios.

In the canonical representation of the qubit depolarizing channel, Bob receives a single qubit, while two qubits dissipate to the environment. We consider three scenarios. If the adversary has full access to the environment (Scenario 1), then we show that covert communication is impossible. On the other hand, if the adversary receives the first qubit, i.e., “half” the environment (Scenario 2), then covert communication turns out to be trivial.

The most interesting case is when the adversary receives the other half (Scenario 3). In this case, the number of information bits that can be transmitted, reliably and covertly, scales as O(√n log⁡n ) when entanglement assistance is available to Alice and Bob, as opposed to O(√n) information bits without assistance. Thereby, we establish that the logarithmic performance boost is not reserved to continuous-variable systems.

M.Sc. student under the supervision of Prof. Uzi Pereg.