Symmetries in quantum networks lead to no-go theorems for entanglement distribution and to verification techniques

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.

22 pages, 18 figures, v2: extended and final version

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Cited by in corpus (24)

• Semidefinite programming relaxations for quantum correlations
• Complex Quantum Networks: a Topical Review
• Analysing quantum systems with randomised measurements
• Quantum-enhanced metrology with network states
• Uncertainty relations from graph theory
• Collective randomized measurements in quantum information processing
• Certifying the Topology of Quantum Networks: Theory and Experiment
• Transformations of Stabilizer States in Quantum Networks
• Detecting Nontrilocal Correlations In Triangle Networks
• Aging and Reliability of Quantum Networks
• Inferring Quantum Network Topology using Local Measurements
• No graph state is preparable in quantum networks with bipartite sources and no classical communication
• Hidden Non n-locality In Linear Networks
• Quantum LOSR networks cannot generate graph states with high fidelity
• Characterizing arbitrary quantum networks in the noisy intermediate-scale quantum era
• Bell inequalities for nonlocality depth
• Metrological usefulness of entanglement and nonlinear Hamiltonians
• Quantum network-entanglement measures
• Multiparticle singlet states cannot be maximally entangled for the bipartitions
• Deformations of the symmetric subspace of qubit chains
• Transformations in quantum networks via local operations assisted by finitely many rounds of classical communication
• Graph state extraction from two-dimensional cluster states
• Frustration graph formalism for qudit observables
• Experimental verification of multi-copy activation of genuine multipartite entanglement