Quantum networks are promising tools for the implementation of long-range quantum communication. The characterization of quantum correlations in networks and their usefulness for information processing is therefore central for the progress of the field, but so far only results for small basic network structures or pure quantum states are known. Here we show that symmetries provide a versatile tool for the analysis of correlations in quantum networks. We provide an analytical approach to characterize correlations in large network structures with arbitrary topologies. As examples, we show that entangled quantum states with a bosonic or fermionic symmetry can not be generated in networks; moreover, cluster and graph states are not accessible. Our methods can be used to design certification methods for the functionality of specific links in a network and have implications for the design of future network structures.
Quantum networks are promising tools for the implementation of long-range quantum communication. The characterization of quantum correlations in networks and their usefulness for information processing is therefore central for the progress of the field, but so far only results for small basic network structures or pure quantum states are known. Here we show that symmetries provide a versatile tool for the analysis of correlations in quantum networks. We provide an analytical approach to characterize correlations in large network structures with arbitrary topologies. As examples, we show that entangled quantum states with a bosonic or fermionic symmetry can not be generated in networks; moreover, cluster and graph states are not accessible. Our methods can be used to design certification methods for the functionality of specific links in a network and have implications for the design of future network structures.
This Thesis contributes to the theory of entanglement distribution in quantum networks, analyzing the generation of long-distance entanglement in particular.We consider that neighboring stations share one partially entangled pair of qubits, which emphasizes the difficulty of creating remote entanglement in realistic settings.The task is then to design local quantum operations at the stations, such that the entanglement present in the links of the whole network gets concentrated between few parties only, regardless of their spatial arrangement.First, we study quantum networks with a two-dimensional lattice structure, where quantum connections between the stations (nodes) are described by non-maximally entangled pure states (links).We show that the generation of a perfectly entangled pair of qubits over an arbitrarily long distance is possible if the initial entanglement of the links is larger than a threshold.This critical value highly depends on the geometry of the lattice, in particular on the connectivity of the nodes, and is related to a classical percolation problem.We then develop a genuine quantum strategy based on multipartite entanglement, improving both the threshold and the success probability of the generation of long-distance entanglement.Second, we consider a mixed-state definition of the connections of the quantum networks.This formalism is well-adapted for a more realistic description of systems in which noise (random errors) inevitably occurs.New techniques are required to create remote entanglement in this setting, and we show how to locally extract and globally process some error syndromes in order to create useful long-distance quantum correlations.Finally, we turn to networks that have a complex topology, which is the case for most real-world communication networks such as the Internet for instance.Besides many other characteristics, these systems have in common the small-world feature, stating that any two nodes are separated by a few links only.Based on the theory of random graphs, we propose a model of quantum complex networks, which exhibit some totally unexpected properties compared to their classical counterparts.5.1 Propagation of a large GHZ state through the lattice . . .5.2 Bit-flip error correction . . . . . . . . . . . . .
To utilize a scalable quantum network and perform a quantum state transfer within distant arbitrary nodes, coherence and control of the dynamics of couplings between the information units must be achieved as a prerequisite ingredient for quantum information processing within a hierarchical structure. Graph theoretic approach provides a powerful tool for the characterization of quantum networks with non-trivial clustering properties. By encoding the topological features of the underlying quantum graphs, relations between the quantum complexity measures are presented revealing the intricate links between a quantum and a classical networks dynamics.
Society relies and depends increasingly on information exchange and communication. In the quantum world, security and privacy is a built-in feature for information processing. The essential ingredient for exploiting these quantum advantages is the resource of entanglement, which can be shared between two or more parties. The distribution of entanglement over large distances constitutes a key challenge for current research and development. Due to losses of the transmitted quantum particles, which typically scale exponentially with the distance, intermediate quantum repeater stations are needed. Here we show how to generalise the quantum repeater concept to the multipartite case, by describing large-scale quantum networks, i.e. network nodes and their long-distance links, consistently in the language of graphs and graph states. This unifying approach comprises both the distribution of multipartite entanglement across the network, and the protection against errors via encoding. The correspondence to graph states also provides a tool for optimising the architecture of quantum networks.
Abstract Characterizing the non-classical correlations of a complex many-body system is an important part of quantum technologies. An ideal tool for this task would scale well with the size of the system, be easily computable and be easily measurable. In this work, we focus on graph states, which are promising platforms for quantum computation, simulation, and metrology. We consider four topologies: star graph states with edges, Turán graphs, r-ary tree graphs, and square grid cluster states. We provide a method to characterize their quantum content: many-body Bell correlations, non-separability and entanglement strength for an arbitrary number of qubits. We also relate the strength of these correlations to the usefulness of graph states for quantum sensing. Finally, we characterize many-body entanglement in graph states with up to eight qubits in 146 classes that are not equivalent under local transformations or graph isomorphisms. This technique is straightforward and does not require any assumptions about the multi-qubit state; therefore it could be applied wherever precise knowledge of many-body quantum correlations is necessary.
We introduce a mapping between graphs and pure quantum bipartite states and show that the associated entanglement entropy conveys non-trivial information about the structure of the graph. Our primary goal is to investigate the family of random graphs known as complex networks. In the case of classical random graphs, we derive an analytic expression for the averaged entanglement entropy while for general complex networks we rely on numerics. For a large number of nodes n we find a scaling where both the prefactor c and the sub-leading O (1) term g e are characteristic of the different classes of complex networks. In particular, g e encodes topological features of the graphs and is named network topological entropy. Our results suggest that quantum entanglement may provide a powerful tool for the analysis of large complex networks with non-trivial topological properties.
The topology of classical networks is determined by physical links between nodes, and after a network request the links are used to establish the desired connections. Quantum networks offer the possibility to generate different kinds of entanglement prior to network requests, which can substitute links and allow one to fulfill multiple network requests with the same resource state. We utilize this to design entanglement-based quantum networks tailored to their desired functionality, independent of the underlying physical structure. The kind of entanglement to be stored is chosen to fulfill all desired network requests (i.e. parallel bipartite or multipartite communications between specific nodes chosen from some finite set), but in such a way that the storage requirement is minimized. This can be accomplished by using multipartite entangled states shared between network nodes that can be transformed by local operations to different target states. We introduce a clustering algorithm to identify connected clusters in the network for a given desired functionality, i.e. the required network topology of the entanglement-based network, and a merging algorithm that constructs multipartite entangled resource states with reduced memory requirement to fulfill all desired network requests. This leads to a significant reduction in required time and resources, and provides a powerful tool to design quantum networks that is unique to entanglement-based networks.