No graph state is preparable in quantum networks with bipartite sources and no classical communication

Abstract

In research concerning quantum networks, it is often assumed that the parties can classically communicate with each other. However, classical communication might introduce a substantial delay to the network, especially if it is large. As the latency of a network is one of its most important characteristics, it is interesting to consider quantum networks in which parties cannot communicate classically and ask what limitations this assumption imposes on the possibility of preparing multipartite states in such networks. We show that graph states of an arbitrary prime local dimension known for their numerous applications in quantum information cannot be generated in a quantum network in which parties are connected via sources of bipartite quantum states and the classical communication is replaced by some pre-shared classical correlations. We then generalise our result to arbitrary quantum states that are sufficiently close to graph states.

15 pages (4.5 + appendices) and 4 figures; See also the related work by Y.-X. Wang et al. arXiv:2208.12100

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Cited by in corpus (7)

• Quantum-enhanced metrology with network states
• Quantum LOSR networks cannot generate graph states with high fidelity
• Quantum network-entanglement measures
• Many-body quantum resources of graph states
• Quantum-assisted Rendezvous on Graphs: Explicit Algorithms and Quantum Computer Simulations
• Graph state extraction from two-dimensional cluster states
• The genuinely multipartite nonlocality of graph states is model-dependent