Higher-order maps and (quantum) network communication

Quantum networks are the fundamental tools to establish terrestrial as well as Satellite communications exploiting the properties of non-classical systems. They are also the backbone of distributive quantum computing. However, our understanding of quantum networks is far from complete, rather, it is in its infancy. In this project, we intend to develop a unified mathematical framework of quantum networks based on higher-order quantum maps and process matrix formalism. This will allow us to understand the properties of quantum networks by defining their capacities based on the particular information processing tasks. We will develop discrimination protocols for quantum networks using higher-order maps and testers to decide the suitable networks for the specific tasks. We will exploit the spatial as well as the temporal correlations offered by quantum networks to have better fidelity of success. An important feature of this formalism is that it generalizes the notion of discrimination of quantum operations. To have a scalable quantum computer, we need to understand the thermodynamic perspective of nano-scale objects. Here, we would like to understand the heat flow through the quantum network by introducing a working principle of a thermal device. We will also use the concept of quantum battery (energy bath) to model the capacity of a quantum network. This will elaborate on our understanding of the open system behavior of quantum networks. As practical implications, we expect that the formalism of quantum networks will allow us -- a) to strengthen the security measures of quantum communication protocols, especially, quantum voting and quantum internet; and b) to have better fidelity in ‘discriminations’ as well as ‘learning’ of quantum operations, using indefinite causal orders.