Abstract
We show how to make quantum networks, both standard and entanglement-based, genuine quantum by providing them with the possibility of handling superposed tasks and superposed addressing. This extension of their functionality relies on a quantum control register, which specifies not only the task of the network, but also the corresponding weights in a coherently superposed fashion. Although adding coherent control to classical tasks, such as sending or measuring—or not doing so—is in general impossible, we introduce protocols that are able to mimick this behavior under certain conditions. We achieve this by always performing the classical task, either on the desired state or a properly chosen dummy state. We provide several examples, and show that externally controlling quantum superposition of tasks offers additional possibilities and advantages over usually considered single functionality. For instance, superpositions of different target state configurations shared among different nodes of the network can be prepared, or quantum information can be sent among a superposition of different paths or to different destinations.
Highlights
Quantum networks promise to be the backbone of upcoming quantum technologies[1,2]
The same is true for the design principles of quantum networks, which are governed by classical approaches
We give a short introduction to Bell-states, GHZ-states and graph states as well as a brief discussion about previous works on quantum networks
Summary
Quantum networks promise to be the backbone of upcoming quantum technologies[1,2]. Several tasks have been identified where quantum effects allow one to obtain an advantage over classical approaches, or even make things possible in the first place. Even though there are some new elements, such as the generation of quantum states or the transmission of quantum information, well-established concepts of classical networks, such as routing or addressing, still appear to be applicable or at least adjustable The latter approach to quantum networks, i.e., a top-down approach, consists of entanglement-based networks, where devices prepare entanglement beforehand, which is subsequently manipulated in order to complete desired requests. This opens different and largely unexplored possibilities, and yields to fully general design principles for quantum networks As we demonstrate, this approach allows for several interesting applications such as the preparation of superpositions of desired target states among different parties of a network, or the completion of network tasks in a coherent way, obtaining, e.g., a superposition of a teleported and non-teleported state. The state after the measurement is, up to local correction operations, given by
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