Parameterized steering criteria via correlation matrices

• URL: http://arxiv.org/abs/2312.05729v1
• Date: Sun, 10 Dec 2023 02:24:03 GMT
• Title: Parameterized steering criteria via correlation matrices
• Authors: Qing-Hua Zhang, Lemin Lai, Shao-Ming Fei
• Abstract summary: We present families of steering criteria for bipartite quantum states in terms of parameterized correlation matrices. We show that these steering criteria may detect more steerable states than the existing steering criteria.
• Score: 2.4940844507983875
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the steerability for arbitrary dimensional bipartite systems based on the correlation matrices given by local special unitary groups. We present families of steering criteria for bipartite quantum states in terms of parameterized correlation matrices. We show that these steering criteria may detect more steerable states than the existing steering criteria. The results are illustrated by detailed examples.

Related papers

• Peres-type Criterion of Einstein-Podolsky-Rosen Steering for Two Qubits [5.478582839093083]
  Quantum nonlocality manifests in multipartite systems through entanglement, Bell's nonlocality, and Einstein-Podolsky-Rosen steering.<n>We show that a Peres-type criterion can be established for EPR steering in the two-qubit system.<n>We prove that this criterion serves as a necessary and sufficient condition for steerability for the Werner state.
  arXiv  Detail & Related papers  (2026-01-17T15:30:39Z)
• Enhanced separability criteria based on symmetric measurements [11.8521376746938]
  We present separability criteria based on local symmetric measurements.<n>We generalize the separability criteria from bipartite to arbitrary multipartite systems.
  arXiv  Detail & Related papers  (2025-12-27T08:05:59Z)
• Cramer-Rao Bounds for Laplacian Matrix Estimation [56.1214184671173]
  We derive closed-form matrix expressions for the Cramer-Rao Bound (CRB) specifically tailored to Laplacian matrix estimation. We demonstrate the use of CRBs in three representative applications: (i) topology identification in power systems, (ii) graph filter identification in diffused models, and (iii) precision matrix estimation in Gaussian Markov random fields under Laplacian constraints.
  arXiv  Detail & Related papers  (2025-04-06T18:28:31Z)
• Induced Covariance for Causal Discovery in Linear Sparse Structures [55.2480439325792]
  Causal models seek to unravel the cause-effect relationships among variables from observed data. This paper introduces a novel causal discovery algorithm designed for settings in which variables exhibit linearly sparse relationships.
  arXiv  Detail & Related papers  (2024-10-02T04:01:38Z)
• Einstein-Podolsky-Rosen Steering Criterion and Monogamy Relation via Correlation Matrices in Tripartite Systems [4.080783151514549]
  The asymmetry of quantum steering makes it vital for one-sided device-independent quantum information processing. We derive a novel and promising steering criterion for any three-qubit states via correlation matrix. We demonstrate the performance of the steering criterion and the monogamy relation by means of several representative examples.
  arXiv  Detail & Related papers  (2024-06-19T07:28:38Z)
• 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)
• Sparsity in Partially Controllable Linear Systems [56.142264865866636]
  We study partially controllable linear dynamical systems specified by an underlying sparsity pattern. Our results characterize those state variables which are irrelevant for optimal control.
  arXiv  Detail & Related papers  (2021-10-12T16:41:47Z)
• GroupifyVAE: from Group-based Definition to VAE-based Unsupervised Representation Disentanglement [91.9003001845855]
  VAE-based unsupervised disentanglement can not be achieved without introducing other inductive bias. We address VAE-based unsupervised disentanglement by leveraging the constraints derived from the Group Theory based definition as the non-probabilistic inductive bias. We train 1800 models covering the most prominent VAE-based models on five datasets to verify the effectiveness of our method.
  arXiv  Detail & Related papers  (2021-02-20T09:49:51Z)
• Nonlinear steering criteria for arbitrary two-qubit quantum systems [16.20946947543463]
  We present some nonlinear steering criteria applicable for arbitrary two-qubit quantum systems and optimized ones for symmetric quantum states. Compared with the existing linear steering criterion and entropic criterion, ours can certify more steerable states without selecting measurement settings or correlation weights.
  arXiv  Detail & Related papers  (2020-09-30T19:57:37Z)
• Experimental demonstration of complementarity relations between quantum steering criteria [17.30189229503516]
  We experimentally verify the complementarity relations between quantum steering criteria by employing two-photon Bell-like states and three Pauli operators. Our results show that the steering criterion based on skew information of coherence is more stronger in detecting the steerability of quantum states.
  arXiv  Detail & Related papers  (2020-07-22T10:17:02Z)
• Understanding Implicit Regularization in Over-Parameterized Single Index Model [55.41685740015095]
  We design regularization-free algorithms for the high-dimensional single index model. We provide theoretical guarantees for the induced implicit regularization phenomenon.
  arXiv  Detail & Related papers  (2020-07-16T13:27:47Z)
• 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 unified framework for spectral clustering in sparse graphs [47.82639003096941]
  We show that a conveniently parametrized form of regularized Laplacian matrix can be used to perform spectral clustering in sparse networks. We also exhibit important connections between this proposed matrix and the now popular non-backtracking matrix, the Bethe-Hessian matrix.
  arXiv  Detail & Related papers  (2020-03-20T10:58:37Z)
• 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.