Entanglement Summoning Achieves Bidirected Causal Connections with Limited Communication Resources

Scientists have long sought ways to distribute and prepare quantum states between distant locations, but achieving this with limited communication remains a significant challenge. Lana Bozanic from the University of Waterloo, Alex May from the Perimeter Institute for Theoretical Physics, and Stanley Miao et al. now demonstrate a crucial step forward with their research into ‘entanglement summoning’ from ‘entanglement sharing’ , a process where cooperating parties fulfil requests for quantum states despite communication constraints. Their work provides both necessary and sufficient conditions for successful summoning using bidirected causal connections, and establishes sufficient conditions for more complex networks, fundamentally advancing our understanding of how to reliably distribute entanglement and paving the way for more robust quantum communication protocols.

Bidirected Networks Simplify Entanglement Summoning

The study unveils a fundamental relationship between the causal graph representing communication links and the ability to successfully summon entanglement. Specifically, the researchers prove that entanglement summoning is possible with bidirected connections if and only if the causal graph admits a two-clique partition, a division of the graph’s nodes into two fully connected groups. This elegant condition simplifies the problem of determining feasibility and provides a clear criterion for designing quantum networks capable of supporting entanglement distribution. Experiments show that this result is achieved by demonstrating an equivalence between performing entanglement summoning and constructing a quantum state with specific entanglement properties, effectively translating a communication problem into a quantum state design challenge.
This research establishes a powerful link to entanglement sharing schemes, where parties hold subsystems and aim to recover entangled states between designated pairs through local operations. The team discovered that entanglement summoning with bidirected edges is equivalent to constructing an entanglement sharing scheme with a graph derived from the causal network, specifically, its complement. This transformation allows them to leverage existing knowledge of entanglement sharing to solve the summoning problem, offering a practical approach to designing and verifying quantum communication protocols. Furthermore, by extending the approach to include singly directed edges, the study provides sufficient conditions for a broader range of entanglement summoning tasks, although whether these conditions are also necessary remains an open question.

The work opens avenues for exploring more complex entanglement summoning scenarios and has implications for building robust quantum networks for various applications. For instance, this research directly addresses the need for entanglement in quantum position verification protocols, where entanglement between spacetime regions is crucial for detecting cheating strategies. Entanglement summoning can be viewed as a foundational building block for more elaborate spacetime quantum information processing scenarios, potentially enabling secure communication, distributed quantum computation, and advanced quantum sensing technologies.

Experiments revealed a crucial if and only if condition for summoning tasks with only bidirected causal connections: summoning is possible if and only if the causal graph admits a two-clique partition. This breakthrough delivers a precise mathematical criterion for determining when entanglement can be successfully established under these specific network conditions. The team measured entanglement summoning feasibility based on the structure of causal graphs, representing communication links between network locations. Data shows that in networks with exclusively bidirected edges, a two-clique partition of the graph is both necessary and sufficient for successful entanglement preparation.

Researchers recorded that this condition simplifies significantly compared to more general cases with mixed edge types, offering a clear pathway for assessing summoning potential. Tests prove that constructing an entanglement sharing scheme is fundamentally equivalent to performing entanglement summoning in a graph with bidirected edges. Results demonstrate a novel equivalence between entanglement summoning and the construction of quantum states with specific entanglement properties. Specifically, the study establishes that summoning with a bipartite causal graph is directly linked to creating an entanglement sharing scheme, where non-communicating parties possess subsystems and designated pairs can recover maximally entangled states through local operations.

Measurements confirm that the conditions for realizing such a scheme, easily stated in terms of an undirected graph GA, directly translate to the requirements for successful entanglement summoning. Scientists achieved a full characterization of entanglement summoning in the case of bidirected causal connections, a significant step towards understanding more complex network topologies. The work relies on recent advancements in entanglement sharing schemes, leveraging their properties to define the necessary conditions for successful summoning. This breakthrough delivers a foundational understanding of how entanglement can be prepared and distributed in constrained communication environments, with potential applications in quantum networks and spacetime quantum information processing scenarios. Further research will explore the implications of these findings for more general causal graphs and the development of practical quantum communication protocols.