Symmetric hypergraph states: Entanglement quantification and robust Bell nonlocality

• URL: http://arxiv.org/abs/2302.01695v1
• Date: Fri, 3 Feb 2023 12:49:32 GMT
• Title: Symmetric hypergraph states: Entanglement quantification and robust Bell nonlocality
• Authors: Jan N\"oller, Otfried G\"uhne, Mariami Gachechiladze
• Abstract summary: We quantify entanglement and nonlocality for large classes of quantum hypergraph states. We recognize the resemblance between symmetric graph states and symmetric hypergraph states.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum hypergraph states are the natural generalization of graph states. Here we investigate and analytically quantify entanglement and nonlocality for large classes of quantum hypergraph states. More specifically, we connect the geometric measure of entanglement of symmetric hypergraphs to their local Pauli stabilizers. As a result we recognize the resemblance between symmetric graph states and symmetric hypergraph states, which explains both, exponentially increasing violation of local realism for infinitely many classes of hypergraph states and its robustness towards particle loss.

Related papers

• Non-symmetric GHZ states; weighted hypergraph and controlled-unitary graph representations [0.0]
  Non-symmetric GHZ states are multipartite entangled states with potential applications in quantum information. We introduce two novel graph formalisms and stabilizers for non-symmetric GHZ states. Our findings enhance the understanding of non-symmetric GHZ states and their potential applications in quantum information science.
  arXiv  Detail & Related papers  (2024-08-05T18:00:18Z)
• Multipartite entanglement sudden death and birth in randomized hypergraph states [0.0]
  We introduce and analyze the entanglement properties of randomized hypergraph states. We show that entanglement exhibits a non-monotonic behavior in terms of the randomness parameters.
  arXiv  Detail & Related papers  (2023-10-31T12:45:26Z)
• Hypergraph Structure Inference From Data Under Smoothness Prior [46.568839316694515]
  We propose a method to infer the probability for each potential hyperedge without labelled data as supervision. We use this prior to derive the relation between the hypergraph structure and the node features via probabilistic modelling. Experiments on both synthetic and real-world data demonstrate that our method can learn meaningful hypergraph structures from data more efficiently than existing hypergraph structure inference methods.
  arXiv  Detail & Related papers  (2023-08-27T18:28:58Z)
• Magic of quantum hypergraph states [6.3109948645563465]
  We analytically investigate the magic resource of archetypal multipartite quantum states -- quantum hypergraph states. Our study advances the understanding of multipartite quantum magic and could lead to applications in quantum computing and quantum many-body physics.
  arXiv  Detail & Related papers  (2023-08-03T17:21:55Z)
• Boundary theories of critical matchgate tensor networks [59.433172590351234]
  Key aspects of the AdS/CFT correspondence can be captured in terms of tensor network models on hyperbolic lattices. For tensors fulfilling the matchgate constraint, these have previously been shown to produce disordered boundary states. We show that these Hamiltonians exhibit multi-scale quasiperiodic symmetries captured by an analytical toy model.
  arXiv  Detail & Related papers  (2021-10-06T18:00:03Z)
• Graph-Theoretic Framework for Self-Testing in Bell Scenarios [37.067444579637076]
  Quantum self-testing is the task of certifying quantum states and measurements using the output statistics solely. We present a new approach for quantum self-testing in Bell non-locality scenarios.
  arXiv  Detail & Related papers  (2021-04-27T08:15:01Z)
• A Thorough View of Exact Inference in Graphs from the Degree-4 Sum-of-Squares Hierarchy [37.34153902687548]
  We tackle the problem of exactly recovering an unknown ground-truth binary labeling of the nodes from a single corrupted observation of each edge. We apply a hierarchy of relaxations known as the sum-of-squares hierarchy, to the problem. We show that the solution of the dual of the relaxed problem is related to finding edge weights of the Johnson and Kneser graphs.
  arXiv  Detail & Related papers  (2021-02-16T08:36:19Z)
• Hamiltonian systems, Toda lattices, Solitons, Lax Pairs on weighted Z-graded graphs [62.997667081978825]
  We identify conditions which allow one to lift one dimensional solutions to solutions on graphs. We show that even for a simple example of a topologically interesting graph the corresponding non-trivial Lax pairs and associated unitary transformations do not lift to a Lax pair on the Z-graded graph.
  arXiv  Detail & Related papers  (2020-08-11T17:58:13Z)
• Hypergraph min-cuts from quantum entropies [1.6312226592634047]
  We prove that the min-cut function of any weighted hypergraph can be approximated by the entropies of quantum states known as stabilizer states. It shows that the recently defined hypergraph cones are contained in the quantum stabilizer entropy cones.
  arXiv  Detail & Related papers  (2020-02-27T19:19:10Z)
• Semi-supervised Anomaly Detection on Attributed Graphs [43.69966808278313]
  We propose a simple yet effective method for detecting anomalous instances on an attribute graph with label information of a small number of instances. The proposed method embeds nodes on the attributed graph in the latent space by taking into account their attributes. In experiments with five real-world attributed graph datasets, we demonstrate that the proposed method achieves better performance than various existing anomaly detection methods.
  arXiv  Detail & Related papers  (2020-02-27T10:06:22Z)
• The Quantum Entropy Cone of Hypergraphs [0.20999222360659606]
  We study hypergraphs and their analogously-defined entropy cones. We find a class of quantum entropy vectors which reach beyond those of holographic states. We show that the hypergraph framework is broadly applicable to the study of entanglement entropy.
  arXiv  Detail & Related papers  (2020-02-13T02:45:28Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.