Speaker: Elyakim Zlotnick
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 continuous-variable 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.
Speaker: Prof. Uzi Pereg
We consider communication over a quantum broadcast channel with cooperation between the receivers. Through this setting, we provide an information-theoretic perspective on quantum repeaters.
First, we observe that entanglement resources alone do not increase the achievable communication rates. By comparison with the recent results by Leditzki et al. (2020), this observation reveals a violation of the BC-MAC duality between the broadcast channel with two receivers and the multiple-access channel with two transmitters.
The next form of cooperation addressed is classical conferencing, where Receiver 1 can send classical messages to Receiver 2. We provide a regularized characterization of the classical capacity region and establish a single-letter formula for the special class of Hadamard broadcast channels. Given both classical conferencing and entanglement resources, Receiver 1 can teleport a quantum state to Receiver 2. This setting is intimately related to quantum repeaters, as the sender, Receiver 1, and Receiver 2 can be viewed as the transmitter, the repeater, and the destination receiver, respectively. When Receiver 1’s sole purpose is to help the transmission to Receiver 2, the model reduces to the quantum primitive relay channel.
We derive lower and upper bounds for each setting; and conclude with observations on the tradeoff between repeater-aided and repeaterless communication, and the bottleneck flow behavior of quantum repeaters.
Speaker: Prof. Uzi Pereg
Communication over a random-parameter quantum channel when the decoder reconstructs the parameter sequence is considered in different scenarios. Regularized formulas are derived for the capacity-distortion regions with strictly-causal, causal, or non-causal channel side information (CSI) available at the encoder, and also without CSI. Single-letter characterizations are established in special cases. In particular, a single-letter formula is given for entanglement-breaking channels when CSI is not available. As a consequence, we obtain regularized formulas for the capacity of random-parameter quantum channels with CSI, generalizing previous results on classical-quantum channels.
