Metrics induced by Jensen-Shannon and related divergences on positive definite matrices

  title={Metrics induced by Jensen-Shannon and related divergences on positive definite matrices},
  author={Suvrit Sra},
  journal={Linear Algebra and its Applications},
  • S. Sra
  • Published 6 November 2019
  • Computer Science
  • Linear Algebra and its Applications

Entropic and trace-distance-based measures of non-Markovianity

The surprising conclusion is reached that the non-Markovianity measure which employs the trace norm of the Helstrom matrix is strictly stronger than all entropic non- Markovianism measures.

Quantum metrics based upon classical Jensen–Shannon divergence

Correlations, Information Backflow, and Objectivity in a Class of Pure Dephasing Models

We critically examine the role that correlations established between a system and fragments of its environment play in characterising the ensuing dynamics. We employ a dephasing model with different

Holevo skew divergence for the characterization of information backflow

This work points to the Holevo quantity as a distinguished quantum divergence to which the formalism can be applied, and shows how several distinct quantifiers of non-Markovianity can be related to each other within this general framework.

The Representation Jensen-R\'enyi Divergence

Numerical experiments involving comparing distributions and applications to sampling unbalanced data for classification show that the proposed measure of divergence can achieve state of the art results.

Generalized Bures-Wasserstein Geometry for Positive Definite Matrices

This paper proposes a generalized Bures-Wasserstein (BW) Riemannian geometry for the manifold of symmetric positive definite matrices. We explore the generalization of the BW geometry in three

Entropic Bounds on Information Backflow.

General upper bounds are derived on the telescopic relative entropy revivals conditioned and determined by the formation of correlations and changes in the environment, considering in particular the Jaynes-Cummings model and a phase covariant dynamics.

Some notes on quantum Hellinger divergences with Heinz means

The information geometry, convexity, in-betweenness property and the barycenter problem of quantum Hellinger divergences with Heinz means is studied. The limiting cases are also considered.



Properties of Classical and Quantum Jensen-Shannon Divergence

It is proved that JDα is the square of a metric for α ∈ (0, 2] , and that the resulting metric space of probability distributions can be isometrically embedded in a real Hilbert space.

Positive definite matrices and the S-divergence

This work introduces the S-divergence as a "natural" distance-like function on the open cone of positive definite matrices and shows that it has several geometric properties similar to those of the Riemannian distance, though without being computationally as demanding.

The metric property of the quantum Jensen-Shannon divergence

Metric character of the quantum Jensen-Shannon divergence

In a recent paper, the generalization of the Jensen-Shannon divergence in the context of quantum theory has been studied [Majtey et al., Phys. Rev. A 72, 052310 (2005)]. This distance between quantum

On the matrix square root via geometric optimization

The primary value of this work is its conceptual value: it shows that for deriving gradient based methods for the matrix square root, the manifold geometric view of positive definite matrices can be much more advantageous than the Euclidean view.

Metrics Induced by Quantum Jensen-Shannon-Renyí and Related Divergences

  • S. Sra
  • Computer Science
  • 2019
This work proves that the square root of symmetric divergences on Hermitian positive definite matrices generated by functions closely related to Pick-Nevanlinna functions is a distance metric.

Logarithmic inequalities under a symmetric polynomial dominance order

  • S. Sra
  • Mathematics
    Proceedings of the American Mathematical Society
  • 2018

Quasi-entropies for finite quantum systems

Inadmissibility of the Usual Estimator for the Mean of a Multivariate Normal Distribution

Abstract : If one observes the real random variables Xi, Xn independently normally distributed with unknown means xi...x in and variance 1, it is customary to estimate xi by Xi. If the loss is the

Nonnegative Matrices and Applications

Preface 1. Perron-Frobenius theory and matrix games 2. Doubly stochastic matrices 3. Inequalities 4. Conditionally positive definite matrices 5. Topics in combinatorial theory 6. Scaling problems and