Related papers: Correlation hypergraph: a new representation of a …
This work is an enquiry into the circumstances under which entropy methods can give an answer to the questions of both quantum separability and classical correlations of a composite state. Several entropy functionals are employed to examine…
Graphs play a crucial role in data mining and machine learning, representing real-world objects and interactions. As graph datasets grow, managing large, decentralized subgraphs becomes essential, particularly within federated learning…
We interpret the Holographic Conjecture in terms of quantum bits (qubits). N-qubit states are associated with surfaces that are punctured in N points by spin networks' edges labeled by the spin-1/2 representation of SU(2), which are in a…
A hypergraph can be obtained from a simplicial complex by deleting some non-maximal simplices. By [11], a hypergraph gives an associated simplicial complex. By [4], the embedded homology of a hypergraph is the homology of the infimum chain…
We present a family of correlations constraints that apply to all multipartite quantum systems of finite dimension. The size of this family is exponential in the number of subsystems. We obtain these relations by defining and investigating…
In passive imaging, one attempts to reconstruct some coefficients in a wave equation from correlations of observed randomly excited solutions to this wave equation. Many methods proposed for this class of inverse problem so far are only…
Hypergraphs naturally represent group interactions, which are omnipresent in many domains: collaborations of researchers, co-purchases of items, and joint interactions of proteins, to name a few. In this work, we propose tools for answering…
Connectivity is a fundamental property of quantum graphs, previously studied in the operator system model for matrix quantum graphs and via graph homomorphisms in the quantum adjacency matrix model. In this paper, we develop an algebraic…
Quantities computed by minimal cuts, such as entanglement entropies achievable by the Ryu-Takayanagi proposal in the AdS/CFT correspondence, are constrained by linear inequalities. We prove a previously conjectured property of all such…
For multivariate data, dependence beyond pair-wise can be important. This is true, for example, in using functional MRI (fMRI) data to investigate brain functional connectivity. When one has more than a few variables, however, the number of…
Quantum coherence and distributed correlations among subparties are often considered as separate, although operationally linked to each other, properties of a quantum state. Here, we propose a measure able to quantify the contributions…
We define correlational (von Neumann) entropy for an individual quantum state of a system whose time-independent hamiltonian contains random parameters and is treated as a member of a statistical ensemble. This entropy is representation…
In a hyper-relational knowledge graph (HKG), each fact is composed of a main triple associated with attribute-value qualifiers, which express additional factual knowledge. The hyper-relational knowledge graph completion (HKGC) task aims at…
We present a self-contained theoretical and computational framework for dynamics following photoexcitation in quantum dots near planar interfaces. A microscopic Hamiltonian parameterized by first principles calculations is merged with a…
Describing and understanding the essence of quantum entanglement and its connection to dynamical chaos is of great scientific interest. In this work, using information geometric (IG) techniques, we investigate the effects of…
We investigate the link between quantum position-verification (QPV) and holography established in [MPS19] using holographic quantum error correcting codes as toy models. By inserting the "temporal" scaling of the AdS metric by hand via the…
I argue that scattering theory for massless particles in Minkowski space should be reformulated as a mapping between past and future representations of an algebra of densities on the conformal boundary. These densities are best thought of…
The construction of large-scale quantum computers will require modular architectures that allow physical resources to be localized in easy-to-manage packages. In this work, we examine the impact of different graph structures on the…
We establish an equivalence between non-isometry of quantum codes and state-dependence of operator reconstruction, and discuss implications of this equivalence for holographic duality. Specifically, we define quantitative measures of…
Graph-theoretic structures play a central role in the description and analysis of quantum systems. In this work, we introduce a new class of quantum states, called $A_\alpha$-graph states, which are constructed from either unweighted or…