Abstract
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.
Highlights
Quantum networks are promising tools for the implementation of long-range quantum communication
Symmetries play an outstanding role in various fields of physics[33] and they have already turned out to be useful for various other problems in quantum information theory[34,35,36,37,38,39,40,41]
We have provided an analytical method to analyze correlations arising in quantum networks from few measurements
Summary
Quantum networks are promising tools for the implementation of long-range quantum communication. We consider states with a permutational (or bosonic) symmetry[36,39,48], obeying relations as in Eq (3) with Π being the projector onto the symmetric subspace. This excludes the preparability of noisy graph states in any network with bipartite sources only.
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