Distributed learning and multi-tier computing are the key ingredients to ensure ultra-reliable and low-latency communication (URLLC) in 6G networks. The distinct transition from connected things in 5G URLLC networks to connected intelligence in 6G URLLC networks requires ultra-secure communication due to the massive amount of private data. However, it is a challenging task to ensure stringent 6G URLLC requirements along with user privacy and data security in distributed networks. In this paper, we devise a distributed quantum computation protocol to perform a nonlocal controlled unitary operation on a bipartite input state in concealed and counterfactual manner and integrate it with anonymous quantum communication networks. This distributed protocol allows Bob to apply an arbitrary singlequbit unitary operator on Alice’s qubit in a controlled and probabilistic fashion, without revealing the operator to her and without transmitting any physical particle over the quantum channel-called the counterfactual concealed telecomputation (CCT). It is shown that the CCT protocol neither requires the preshared entanglement nor depends on the bipartite input state and that the single-qubit unitary teleportation is a special case of CCT. The quantum circuit for CCT can be implemented using the (chained) quantum Zeno gates. The protocol becomes deterministic with simplified circuit implementation if the initial composite state of Alice and Bob is a Bell-type state. Furthermore, we provide numerical examples of quantum anonymous broadcast networks using the CCT protocol and show their degrees of anonymity in the presence of malicious users.

We discuss discrete Weyl channels (DWCs) with correlated noise in consecutive uses. Some special cases of DWCs have been shown to have the so-called transition behavior, where the optimal signal states, which maximize the Holevo information between the transmitter and the receiver, sharply transition from product states to maximally entangled states as the degree of memory between the consecutive channel uses increases from a threshold value. We first show the general existence of this transition behavior for a class of DWCs where the product states are optimal for the memoryless case. We also provide two methods to estimate the degree of memory exhibited by the correlated noise. These estimators rely on generating classical data by measuring the channel output which shows the same memory characteristics as the consecutive uses of the channel. We specifically consider the Markovian noise but one of our proposed estimators can be straightforwardly generalized to an arbitrary type of noise as it provides the direct access to the sequence in which noise affects the consecutive input states.