Polar coding is a method for communication over noisy classical channels, which is provably capacity achieving and has an efficient encoding and decoding. Recently, this method has been generalized to the realm of quantum information processing, for tasks such as classical communication, private classical communication, and quantum communication. In this paper, we apply the polar coding method to network classical-quantum information theory, by making use of recent advances for related classical tasks. In particular, we consider problems such as the compound multiple access channel and the quantum interference channel. The main result of our work is that it is possible to achieve the best known inner bounds on the achievable rate regions for these tasks, without requiring a so-called quantum simultaneous decoder. Thus, this paper paves the way for developing network classical-quantum information theory further without requiring a quantum simultaneous decoder.

We present a new achievable rate region for the two-user binary-input classical-quantum broadcast channel. The result is a generalization of the classical Marton-Gelfand-Pinsker region and is provably larger than the best previously known rate region for classical-quantum broadcast channels. The proof of achievability is based on the recently introduced polar coding scheme and its generalization to quantum network information theory.

Proving achievability of protocols in quantum Shannon theory usually does not consider the efficiency at which the goal of the protocol can be achieved. Nevertheless it is known that protocols such as coherent state merging are efficiently achievable at optimal rate.We aim to investigate this fact further in a general one-shot setting, by considering certain classes of decoupling theorems and give exact rates for these classes. Moreover we compare results of general decoupling theorems using Haar distributed unitaries with those using smaller sets of operators, in particular ε-approximate 2-designs. We also observe the behavior of our rates in special cases such as ε approaching zero and the asymptotic limit.

We exhibit a possible road toward a strong converse for the quantum capacity of degradable channels. In particular, we show that all degradable channels obey what we call a “pretty strong” converse: when the code rate increases above the quantum capacity, the fidelity makes a discontinuous jump from 1 to at most 1/√2, asymptotically. A similar result can be shown for the private (classical) capacity. Furthermore, we can show that if the strong converse holds for symmetric channels (which have quantum capacity zero), then degradable channels obey the strong converse. The above-mentioned asymptotic jump of the fidelity at the quantum capacity then decreases from 1 to 0.

We exhibit a possible road towards a strong converse for the quantum capacity of degradable channels. In particular, we show that all degradable channels obey what we call a “pretty strong” converse: When the code rate increases above the quantum capacity, the fidelity makes a discontinuous jump from 1 to at most 1/√2, asymptotically. A similar result can be shown for the private (classical) capacity. Furthermore, we can show that if the strong converse holds for symmetric channels (which have quantum capacity zero), then degradable channels obey the strong converse: The above-mentioned asymptotic jump of the fidelity at the quantum capacity is then from 1 down to 0.