Inflated Graph States Refuting Communication-Assisted LHV Models

• URL: http://arxiv.org/abs/2210.07068v1
• Date: Thu, 13 Oct 2022 14:49:32 GMT
• Title: Inflated Graph States Refuting Communication-Assisted LHV Models
• Authors: Uta Isabella Meyer, Fr\'ed\'eric Grosshans, Damian Markham
• Abstract summary: correlations from Pauli measurements on certain network graphs refute a local hidden variable description even allowing some communication along the graph. This has recently found applications in proving separation between classical and quantum computing. In this work, we propose systematic extensions of any graph state, which we dub inflated graph states such that they exhibit correlations which refute any communication assisted LHV model.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Standard Bell inequalities hold when distant parties are not allowed to communicate. Barrett et al. found correlations from Pauli measurements on certain network graphs refute a local hidden variable (LHV) description even allowing some communication along the graph. This has recently found applications in proving separation between classical and quantum computing, in terms of shallow circuits, and distributed computing. The correlations presented by Barrett et al. can be understood as coming from an extension of three party GHZ state correlations which can be embedded on a graph state. In this work, we propose systematic extensions of any graph state, which we dub inflated graph states such that they exhibit correlations which refute any communication assisted LHV model. We further show the smallest possible such example, with a 7-qubit linear graph state, as well as specially crafted smaller examples with 5 and 4 qubits. The latter is the smallest possible violation using binary inputs and outputs.

Related papers

• Graph-Dictionary Signal Model for Sparse Representations of Multivariate Data [49.77103348208835]
  We define a novel Graph-Dictionary signal model, where a finite set of graphs characterizes relationships in data distribution through a weighted sum of their Laplacians. We propose a framework to infer the graph dictionary representation from observed data, along with a bilinear generalization of the primal-dual splitting algorithm to solve the learning problem. We exploit graph-dictionary representations in a motor imagery decoding task on brain activity data, where we classify imagined motion better than standard methods.
  arXiv  Detail & Related papers  (2024-11-08T17:40:43Z)
• Distinguishing Graph States by the Properties of Their Marginals [0.0]
  We introduce a family of easy-to-compute LU-invariants based on the marginal structure of the graphs. We show that these invariants can uniquely identify all LU-orbits and entanglement classes of every graph state of 8 qubits or less. We also discuss examples of entanglement classes with more nodes, where their marginal structure does not allow us to tell them apart.
  arXiv  Detail & Related papers  (2024-06-14T12:03:10Z)
• Self-Testing Graph States Permitting Bounded Classical Communication [1.2499537119440245]
  We show that certain graph states can be robustly self-tested even allowing for communication. We provide an explicit self-test for the circular graph state and the honeycomb cluster state.
  arXiv  Detail & Related papers  (2024-04-04T14:53:17Z)
• Useful entanglement can be extracted from noisy graph states [0.0]
  Cluster states and graph states in general offer a useful model of the stabilizer formalism.<n>We leverage both properties to design feasible families of states that can be used as robust building blocks of quantum computation.<n>We show that robust entanglement can be extracted by proper design of the linear graph with only a minimal overhead of the physical qubits.
  arXiv  Detail & Related papers  (2024-02-01T19:00:05Z)
• Multipartite Entanglement Distribution in Quantum Networks using Subgraph Complementations [9.32782060570252]
  We propose a novel approach for distributing graph states across a quantum network. We show that the distribution of graph states can be characterized by a system of subgraph complementations. We find a close to optimal sequence of subgraph complementation operations to distribute an arbitrary graph state.
  arXiv  Detail & Related papers  (2023-08-25T23:03:25Z)
• Graphon Pooling for Reducing Dimensionality of Signals and Convolutional Operators on Graphs [131.53471236405628]
  We present three methods that exploit the induced graphon representation of graphs and graph signals on partitions of [0, 1]2 in the graphon space. We prove that those low dimensional representations constitute a convergent sequence of graphs and graph signals. We observe that graphon pooling performs significantly better than other approaches proposed in the literature when dimensionality reduction ratios between layers are large.
  arXiv  Detail & Related papers  (2022-12-15T22:11:34Z)
• Graph-in-Graph (GiG): Learning interpretable latent graphs in non-Euclidean domain for biological and healthcare applications [52.65389473899139]
  Graphs are a powerful tool for representing and analyzing unstructured, non-Euclidean data ubiquitous in the healthcare domain. Recent works have shown that considering relationships between input data samples have a positive regularizing effect for the downstream task. We propose Graph-in-Graph (GiG), a neural network architecture for protein classification and brain imaging applications.
  arXiv  Detail & Related papers  (2022-04-01T10:01:37Z)
• Explicit Pairwise Factorized Graph Neural Network for Semi-Supervised Node Classification [59.06717774425588]
  We propose the Explicit Pairwise Factorized Graph Neural Network (EPFGNN), which models the whole graph as a partially observed Markov Random Field. It contains explicit pairwise factors to model output-output relations and uses a GNN backbone to model input-output relations. We conduct experiments on various datasets, which shows that our model can effectively improve the performance for semi-supervised node classification on graphs.
  arXiv  Detail & Related papers  (2021-07-27T19:47:53Z)
• Hyperbolic Graph Embedding with Enhanced Semi-Implicit Variational Inference [48.63194907060615]
  We build off of semi-implicit graph variational auto-encoders to capture higher-order statistics in a low-dimensional graph latent representation. We incorporate hyperbolic geometry in the latent space through a Poincare embedding to efficiently represent graphs exhibiting hierarchical structure.
  arXiv  Detail & Related papers  (2020-10-31T05:48:34Z)
• Factorizable Graph Convolutional Networks [90.59836684458905]
  We introduce a novel graph convolutional network (GCN) that explicitly disentangles intertwined relations encoded in a graph. FactorGCN takes a simple graph as input, and disentangles it into several factorized graphs. We evaluate the proposed FactorGCN both qualitatively and quantitatively on the synthetic and real-world datasets.
  arXiv  Detail & Related papers  (2020-10-12T03:01:40Z)
• Verification of graph states in an untrusted network [0.0]
  We consider verification of graph states generated by an untrusted source and shared between a network of possibly dishonest parties. This has implications in certifying the application of graph states for various distributed tasks. We present a protocol which is globally efficient for a large family of useful graph states.
  arXiv  Detail & Related papers  (2020-07-26T13:17:21Z)
• Generation and Robustness of Quantum Entanglement in Spin Graphs [0.0]
  Entanglement is a crucial resource for quantum information processing. We show how a graph structure can be used to generate high fidelity entangled states. We also investigate how fabrication errors affect the entanglement generation protocol.
  arXiv  Detail & Related papers  (2020-02-18T16:11:57Z)

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.