## 2 Citations

### 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.

## 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…