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We introduce a novel model of multipartite entanglement based on topological links, generalizing the graph/hypergraph entropy cone program. We demonstrate that there exist link representations of entropy vectors which provably cannot be represented by graphs or hypergraphs. Furthermore, we show that the contraction map proof method generalizes to the topological setting, though now requiring oracular solutions to well-known but difficult problems in knot theory. 

In this work, we generalize the graph-theoretic techniques used for the holographic entropy cone to study hypergraphs and their analogously-defined entropy cone.This allows us to develop a framework to efficiently compute entropies and prove inequalities satisfied by hypergraphs.In doing so, we discover a class of quantum entropy vectors which reach beyond those of holographic states and obey constraints intimately related to the ones obeyed by stabilizer states and linear ranks.We show that, at least up to 4 parties, the hypergraph cone is identical to the stabilizer entropy cone, thus demonstrating that the hypergraph framework is broadly applicable to the study of entanglement entropy.We conjecture that this equality continues to hold for higher party numbers and report on partial progress on this direction.To physically motivate this conjectured equivalence, we also propose a plausible method inspired by tensor networks to construct a quantum state from a given hypergraph such that their entropy vectors match. 

Deformable energy devices capable of efficiently scavenging ubiquitous mechanical signals enable the realization of self-powered wearable electronic systems for emerging human-integrated technologies. Triboelectric nanogenerators (TENGs) utilizing soft polymers with embedded additives and engineered dielectric properties emerge as ideal candidates for such applications. However, the use of solid filler materials in the state-of-the-art TENGs limits the devices' mechanical deformability and long-term durability. The current structural design for TENGs faces the dilemma where the enhanced dielectric constant of the TENG's contact layer leads to an undesirable saturation of the surface charge density. Here, we present a novel scheme to address the above issues, by exploring a liquid-metal-inclusion based TENG (LMI-TENG) where inherently deformable core–shell LMIs are incorporated into wearable high-dielectric-constant polymers. Through a holistic approach integrating theoretical and experimental efforts, we identified the parameter space for designing an LMI-TENG with co-optimized output and mechanical deformability. As a proof of concept, we demonstrated an LMI-TENG based wireless media control system for a self-powered user interface. The device architecture and design scheme presented here provide a promising solution towards the realization of self-powered human-integrated technologies.