相关论文: Correlation hypergraph: a new representation of a …
Interactions govern the flow of information and the formation of correlations in quantum systems, dictating the phases of matter found in nature and the forms of entanglement generated in the laboratory. Typical interactions decay with…
The density matrix of composite spin system is discussed in relation to the adjoint representation of unitary group U(n). The entanglement structure is introduced as an additional ingredient to the description of the linear space carrying…
We establish a holographic duality between d-dimensional mixed-state symmetry-protected topological phases (mSPTs) and (d+1)-dimensional subsystem symmetry-protected topological states (SSPTs). Specifically, we show that the reduced density…
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…
We develop a reinforcement learning algorithm to study the holographic entropy cone. Given a target entropy vector, our algorithm searches for a graph realization whose min-cut entropies match the target vector. If the target vector does…
Hypergraphs, capable of representing high-order interactions via hyperedges, have become a powerful tool for modeling real-world biological and social systems. Inherent relationships within these real-world systems, such as the encoding…
This PhD thesis lays out algebraic and topological structures relevant for the study of probabilistic graphical models. Marginal estimation algorithms are introduced as diffusion equations of the form $\dot u = \delta \varphi$. They…
Characterizing anisotropic correlations in quantum and statistical systems requires a coordinate-invariant framework. We introduce a geometric map based on the local informational line element, calibrated by the Euclidean benchmark scale…
In this paper we develop a framework to study observability for uniform hypergraphs. Hypergraphs, being extensions of graphs, allow edges to connect multiple nodes and unambiguously represent multi-way relationships which are ubiquitous in…
According to the holographic principle, the information content assigned to a gravitational region is processed by its lower dimensional boundary. As an example setup compatible with this principle, the AdS/CFT correspondence relies on the…
We introduce a nonparametric graphical model for discrete node variables based on additive conditional independence. Additive conditional independence is a three way statistical relation that shares similar properties with conditional…
We study quantum coarse-grained entropy and demonstrate that the gap in entropy between local and global coarse-grainings is a natural generalization of entanglement entropy to mixed states and multipartite systems. This "quantum…
Testing (conditional) independence of multivariate random variables is a task central to statistical inference and modelling in general - though unfortunately one for which to date there does not exist a practicable workflow. State-of-art…
Hypergraph visualization has many applications in network data analysis. Recently, a polygon-based representation for hypergraphs has been proposed with demonstrated benefits. However, the polygon-based layout often suffers from excessive…
In this work, we present a comprehensive exploration of the entanglement and graph connectivity properties of graph states. We quantify the entanglement in pseudo graph states using the entanglement distance, a recently introduced measure…
We discuss the time dependence of subsystem entropies in interacting quantum systems. As a model for the time dependence, we suggest that the entropy is as large as possible given two constraints: one follows from the existence of an…
This paper, based on the interdisciplinary frontiers of quantum electrodynamics, causal set theory, and the AdS/CFT holographic duality, integrates Keppler's zero point field resonance theory, the discrete causal structure and horizon…
We study a topological field theory in four dimensions on a manifold with boundary. A bulk-boundary interaction is introduced through a novel variational principle rather than explicitly. Through this scheme we find that the boundary values…
We extensively explore the connections between time-like entanglement and non-hermitian density matrices in quantum many-body systems. We classify setups where we encounter non-hermitian density matrices into two types: one is due to causal…
Quantum networks are important for quantum communication, enabling tasks such as quantum teleportation, quantum key distribution, quantum sensing, and quantum error correction, often utilizing graph states, a specific class of multipartite…