Proximity-induced fine features and spin-textures of the electronic bands in graphene-based van der Waals heterostructures can be explored from the point of tailoring a twist angle. Here we study spin–orbit coupling and exchange coupling engineering of graphene states in the proximity of 1T-TaS 2 not triggering the twist, but a charge density wave (CDW) in 1T-TaS 2 —a realistic low-temperature phase. Using density functional theory and effective model we found that the emergence of the CDW in 1T-TaS 2 significantly enhances Rashba spin–orbit splitting in graphene and tilts the spin texture by a significant Rashba angle—in a very similar way as in the conventional twist-angle scenarios. Moreover, the partially filled Ta d-band in the CDW phase leads to the spontaneous emergence of the in-plane magnetic order that transgresses via proximity from 1T-TaS 2 to graphene, hence, simultaneously superimposing along the spin–orbit also the exchange coupling proximity effect. To describe this intricate proximity landscape we have developed an effective model Hamiltonian and provided a minimal set of parameters that excellently reproduces all the spectral features predicted by the first-principles calculations. Conceptually, the CDW provides a highly interesting knob to control the fine features of electronic states and to tailor the superimposed proximity effects—a sort of twistronics without twist.

We address the question of the existence of quantum channels that are divisible in two quantum channels but not in three or, more generally, channels divisible in n but not in n þ 1 parts. We show that for the qubit those channels do not exist, whereas for general finite-dimensional quantum channels the same holds at least for full Kraus rank channels. To prove these results, we introduce a novel decomposition of quantum channels which separates them into a boundary and Markovian part, and it holds for any finite dimension. Additionally, the introduced decomposition amounts to the well-known connection between divisibility classes and implementation types of quantum dynamical maps and can be used to implement quantum channels using smaller quantum registers.

Quantum networks have been shown to connect users with full-mesh topologies without trusted nodes. We present advancements on our scalable polarisation entanglement-based quantum network testbed, which has the ability to perform protocols beyond simple quantum key distribution. Our approach utilises wavelength multiplexing, which is ideal for quantum networks across local metropolitan areas due to the ease of connecting additional users to the network without increasing the resource requirements per user. We show a 10 user fully connected quantum network with metropolitan scale deployed fibre links, demonstrating polarisation stability and the ability to generate secret keys over a period of 10.8 days with a network wide average-effective secret key rate of 3.38 bps.