On the covariance matrix for Gaussian states
- URL: http://arxiv.org/abs/2003.11063v2
- Date: Sat, 28 Mar 2020 22:48:27 GMT
- Title: On the covariance matrix for Gaussian states
- Authors: Angel Garcia-Chung
- Abstract summary: We discuss how the criteria to characterize squeezing and entanglement using the covariance matrix give rise to new criteria in the symplectic matrix elements used to construct the general Gaussian states.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We show the explicit expression for the covariance matrix of general Gaussian
states in terms of the symplectic group matrices. We discuss how the criteria
to characterize squeezing and entanglement using the covariance matrix give
rise to new criteria in the symplectic matrix elements used to construct the
general Gaussian states.
Related papers
- Understanding Matrix Function Normalizations in Covariance Pooling through the Lens of Riemannian Geometry [63.694184882697435]
Global Covariance Pooling (GCP) has been demonstrated to improve the performance of Deep Neural Networks (DNNs) by exploiting second-order statistics of high-level representations.
arXiv Detail & Related papers (2024-07-15T07:11:44Z) - A Result About the Classification of Quantum Covariance Matrices Based
on Their Eigenspectra [0.0]
We find a non-trivial class of eigenspectra with the property that the set of quantum covariance matrices corresponding to any eigenspectrum in this class are related by symplectic transformations.
We show that all non-degenerate eigenspectra with this property must belong to this class, and that the set of such eigenspectra coincides with the class of non-degenerate eigenspectra.
arXiv Detail & Related papers (2023-08-07T09:40:09Z) - Quantitative deterministic equivalent of sample covariance matrices with
a general dependence structure [0.0]
We prove quantitative bounds involving both the dimensions and the spectral parameter, in particular allowing it to get closer to the real positive semi-line.
As applications, we obtain a new bound for the convergence in Kolmogorov distance of the empirical spectral distributions of these general models.
arXiv Detail & Related papers (2022-11-23T15:50:31Z) - Thermal equilibrium in Gaussian dynamical semigroups [77.34726150561087]
We characterize all Gaussian dynamical semigroups in continuous variables quantum systems of n-bosonic modes which have a thermal Gibbs state as a stationary solution.
We also show that Alicki's quantum detailed-balance condition, based on a Gelfand-Naimark-Segal inner product, allows the determination of the temperature dependence of the diffusion and dissipation matrices.
arXiv Detail & Related papers (2022-07-11T19:32:17Z) - Semi-Supervised Subspace Clustering via Tensor Low-Rank Representation [64.49871502193477]
We propose a novel semi-supervised subspace clustering method, which is able to simultaneously augment the initial supervisory information and construct a discriminative affinity matrix.
Comprehensive experimental results on six commonly-used benchmark datasets demonstrate the superiority of our method over state-of-the-art methods.
arXiv Detail & Related papers (2022-05-21T01:47:17Z) - Riemannian statistics meets random matrix theory: towards learning from
high-dimensional covariance matrices [2.352645870795664]
This paper shows that there seems to exist no practical method of computing the normalising factors associated with Riemannian Gaussian distributions on spaces of high-dimensional covariance matrices.
It is shown that this missing method comes from an unexpected new connection with random matrix theory.
Numerical experiments are conducted which demonstrate how this new approximation can unlock the difficulties which have impeded applications to real-world datasets.
arXiv Detail & Related papers (2022-03-01T03:16:50Z) - Detection of tripartite entanglement based on principal basis matrix
representations [1.3319340093980596]
We study the entanglement in tripartite quantum systems by using the principal basis matrix representations of density matrices.
Detailed examples show that our method can detect more entangled states than previous ones.
arXiv Detail & Related papers (2022-02-13T01:25:37Z) - Symplectic decomposition from submatrix determinants [0.0]
An important theorem in Gaussian quantum information tells us that we can diagonalise the covariance matrix of any Gaussian state via a symplectic transformation.
Inspired by a recently presented technique for finding the eigenvectors of a Hermitian matrix from certain submatrix eigenvalues, we derive a similar method for finding the diagonalising symplectic from certain submatrix determinants.
arXiv Detail & Related papers (2021-08-11T18:00:03Z) - Adversarially-Trained Nonnegative Matrix Factorization [77.34726150561087]
We consider an adversarially-trained version of the nonnegative matrix factorization.
In our formulation, an attacker adds an arbitrary matrix of bounded norm to the given data matrix.
We design efficient algorithms inspired by adversarial training to optimize for dictionary and coefficient matrices.
arXiv Detail & Related papers (2021-04-10T13:13:17Z) - Optimal Iterative Sketching with the Subsampled Randomized Hadamard
Transform [64.90148466525754]
We study the performance of iterative sketching for least-squares problems.
We show that the convergence rate for Haar and randomized Hadamard matrices are identical, andally improve upon random projections.
These techniques may be applied to other algorithms that employ randomized dimension reduction.
arXiv Detail & Related papers (2020-02-03T16:17:50Z) - Relative Error Bound Analysis for Nuclear Norm Regularized Matrix Completion [101.83262280224729]
We develop a relative error bound for nuclear norm regularized matrix completion.
We derive a relative upper bound for recovering the best low-rank approximation of the unknown matrix.
arXiv Detail & Related papers (2015-04-26T13:12:16Z)
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.