A unifying separability criterion based on extended correlation tensor

• URL: http://arxiv.org/abs/2406.17230v1
• Date: Tue, 25 Jun 2024 02:36:28 GMT
• Title: A unifying separability criterion based on extended correlation tensor
• Authors: Xiaofen Huang, Tinggui Zhang, Naihuan Jing,
• Abstract summary: Entanglement is fundamental inasmuch because it rephrases the quest for the classical-quantum demarcation line. We introduce and formulate a practicable criterion for separability based on the correlation tensor.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Entanglement is fundamental inasmuch because it rephrases the quest for the classical-quantum demarcation line, and it also has potentially enormous practical applications in modern information technology. In this work, employing the approach of matrix decomposition, we introduce and formulate a practicable criterion for separability based on the correlation tensor. It is interesting that this criterion unifies several relevant separability criteria proposed before, even stronger than some of them. Theoretical analysis and detailed examples demonstrate its availability and feasibility for entanglement detection. Furthermore we build a family of entanglement witnesses using the criterion according to its linearity in the density operator space.

Related papers

• Generalized Criterion for Identifiability of Additive Noise Models Using Majorization [7.448620208767376]
  We introduce a novel identifiability criterion for directed acyclic graph (DAG) models. We demonstrate that this criterion extends and generalizes existing identifiability criteria. We present a new algorithm for learning a topological ordering of variables.
  arXiv  Detail & Related papers  (2024-04-08T02:18:57Z)
• Synergistic eigenanalysis of covariance and Hessian matrices for enhanced binary classification [72.77513633290056]
  We present a novel approach that combines the eigenanalysis of a covariance matrix evaluated on a training set with a Hessian matrix evaluated on a deep learning model. Our method captures intricate patterns and relationships, enhancing classification performance.
  arXiv  Detail & Related papers  (2024-02-14T16:10:42Z)
• Applications of flow models to the generation of correlated lattice QCD ensembles [69.18453821764075]
  Machine-learned normalizing flows can be used in the context of lattice quantum field theory to generate statistically correlated ensembles of lattice gauge fields at different action parameters. This work demonstrates how these correlations can be exploited for variance reduction in the computation of observables.
  arXiv  Detail & Related papers  (2024-01-19T18:33:52Z)
• Nonparametric Partial Disentanglement via Mechanism Sparsity: Sparse Actions, Interventions and Sparse Temporal Dependencies [58.179981892921056]
  This work introduces a novel principle for disentanglement we call mechanism sparsity regularization. We propose a representation learning method that induces disentanglement by simultaneously learning the latent factors. We show that the latent factors can be recovered by regularizing the learned causal graph to be sparse.
  arXiv  Detail & Related papers  (2024-01-10T02:38:21Z)
• Characterizing Hybrid Causal Structures with the Exclusivity Graph Approach [0.41942958779358674]
  We extend a graph theoretical technique to explore classical, quantum, and no-signaling distributions in hybrid scenarios. We show how with our method we can construct minimal Bell-like inequalities capable of simultaneously distinguishing classical, quantum, and no-signaling behaviors. The demonstrated method will represent a powerful tool to study quantum networks and for applications in quantum information tasks.
  arXiv  Detail & Related papers  (2023-12-29T19:44:38Z)
• On genuine entanglement for tripartite systems [13.283754041776882]
  We first derive an analytical sufficient criterion to detect genuine entanglement of tripartite qubit quantum states. We then use the norm of correlation tensors to study genuine entanglement for tripartite qudit quantum states.
  arXiv  Detail & Related papers  (2022-09-11T01:55:59Z)
• 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)
• Discovering Latent Causal Variables via Mechanism Sparsity: A New Principle for Nonlinear ICA [81.4991350761909]
  Independent component analysis (ICA) refers to an ensemble of methods which formalize this goal and provide estimation procedure for practical application. We show that the latent variables can be recovered up to a permutation if one regularizes the latent mechanisms to be sparse.
  arXiv  Detail & Related papers  (2021-07-21T14:22:14Z)
• Localisation in quasiperiodic chains: a theory based on convergence of local propagators [68.8204255655161]
  We present a theory of localisation in quasiperiodic chains with nearest-neighbour hoppings, based on the convergence of local propagators. Analysing the convergence of these continued fractions, localisation or its absence can be determined, yielding in turn the critical points and mobility edges. Results are exemplified by analysing the theory for three quasiperiodic models covering a range of behaviour.
  arXiv  Detail & Related papers  (2021-02-18T16:19:52Z)
• Separability criteria based on Bloch representation of density matrices [1.4550422197805504]
  We first derive the norms of the correlation tensors and obtain the necessary conditions for separability under partition of tripartite and four-partite quantum states. Using detailed examples, our results are seen to be able to detect more entangled states than previous studies.
  arXiv  Detail & Related papers  (2020-04-24T04:11:54Z)
• A family of multipartite separability criteria based on correlation tensor [0.0]
  A family of separability criteria based on correlation matrix (tensor) is provided. It unifies several criteria known before like e.g. CCNR or realignment criterion, de Vicente criterion and derived recently separability criterion based on SIC POVMs.
  arXiv  Detail & Related papers  (2020-01-22T20:16:18Z)

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.