## 10 Citations

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

- Computer SciencePhysical Review A
- 2022

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.

### Probabilistic damage localization by empirical data analysis and symmetric information measure

- Measurement
- 2022

### Quantum metrics based upon classical Jensen–Shannon divergence

- Computer SciencePhysica A: Statistical Mechanics and its Applications
- 2022

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

- PhysicsEntropy
- 2022

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

- Computer SciencePhysical Review A
- 2022

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

- Computer Science, Mathematics
- 2021

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

- Mathematics
- 2021

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.

- Computer SciencePhysical review letters
- 2021

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

- Mathematics
- 2020

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.

## References

SHOWING 1-10 OF 31 REFERENCES

### Properties of Classical and Quantum Jensen-Shannon Divergence

- Computer Science
- 2008

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

- Computer Science
- 2011

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

- Philosophy, Computer ScienceAdvances in Mathematics
- 2021

### Metric character of the quantum Jensen-Shannon divergence

- Physics
- 2008

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

- Computer Science
- 2015

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

- Computer ScienceArXiv
- 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

- MathematicsProceedings of the American Mathematical Society
- 2018

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

- Mathematics
- 1956

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

- Mathematics, Economics
- 1997

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…