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arXiv:2108.08176 · Physical Review A

Cost and routing of continuous-variable quantum networks

Federico Centrone, Frédéric Grosshans, Valentina Parigi

Published Oct 20, 2023• 14 citations
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Abstract

The authors give insight into the amount of entanglement that can be achieved from Gaussian graph states as well as the amount of squeezing required to prepare them. They find that these quantities are highly dependent on the structure of the quantum network.
DOI
10.1103/physreva.108.042615

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Large-scale operations in quantum networks require efficient sorting of desired paths between nodes. In this article, we consider entanglement routing, which involves establishing an entanglement link between specific nodes in a large network of bosonic nodes. The networks are continuous-variable graph states built from finite squeezing and passive linear optics, shaped by complex network structures that mimic real-world networks. We construct a bipartite routing protocol with the specific goal of establishing a teleportation channel between two clients via passive optics operations locally operated by two different providers sharing the network. We provide criteria for extracting the aforementioned channel and, through the use of a derandomised evolutionary algorithm, extend the existing framework to study complex graph topologies.
Complex networks structures have been extensively used for describing complex natural and technological systems, like the Internet or social networks. More recently, complex network theory has been applied to quantum systems, where complex network topologies may emerge in multiparty quantum states and quantum algorithms have been studied in complex graph structures. In this work, we study multimode Continuous Variables entangled states, named cluster states, where the entanglement structure is arranged in typical real-world complex networks shapes. Cluster states are a resource for measurement-based quantum information protocols, where the quality of a cluster is assessed in terms of the minimal amount of noise it introduces in the computation. We study optimal graph states that can be obtained with experimentally realistic quantum resources, when optimized via analytical procedure. We show that denser and regular graphs allow for better optimization. In the spirit of quantum routing, we also show the reshaping of entanglement connections in small networks via linear optics operations based on numerical optimization.
Multimode entangled pure Gaussian states are an essential resource for continuous variable (CV) quantum information processing. Menicucci et al. [2011] have shown how to describe them as graphs with complex adjacency matrices. Among such complex graph states (CGSs), quantum optics experimental setups straightforwardly display correlations described by purely imaginary graph states (iRGSs) whereas theoretical literature favors off-diagonal real graph state (RGS) descriptions, which actually reflect the entanglement structure in the infinite squeezing limit [Gonzalez-Arciniegas et al. 2021]. We study them beyond this ideal case, thus establishing in the finite squeezing regime an equivalence criterion for the generic case of CGSs through a graph propagating set of conditions which either finds a Gaussian Local Unitary (GLU) converting one state to another or gives a proof of impossibility if such a GLU does not exist. In the experimentally relevant case of the conversion between iRGSs and RGSs, the set of conditions results in simple relations between the topologies of the equivalent real and imaginary graphs. Finally, we show that the canonical forms of iRGSs and RGSs imply that the topology of the CV real and imaginary graph states are too rigid to admit any exact qumode local-addition analogue to the qubit complementation or qudit local-addition, thus demonstrating the non-existence of any exact qumode local-addition for these states. We however define an approximate one when the squeezing is strong enough.