# Minimizing Quantum Renyi Divergences via Mirror Descent with Polyak Step Size

@article{You2021MinimizingQR, title={Minimizing Quantum Renyi Divergences via Mirror Descent with Polyak Step Size}, author={Jun-Kai You and Hao-Chung Cheng and Yen-Huan Li}, journal={ArXiv}, year={2021}, volume={abs/2109.06054} }

Quantum information quantities play a substantial role in characterizing operational quantities in various quantum information-theoretic problems. We consider numerical computation of four quantum information quantities: Petz-Augustin information, sandwiched Augustin information, conditional sandwiched Rényi entropy and sandwiched Rényi information. To compute these quantities requires minimizing some order-α quantum Rényi divergences over the set of quantum states. Whereas the optimization… Expand

#### References

SHOWING 1-10 OF 55 REFERENCES

Properties of Scaled Noncommutative Rényi and Augustin Information

- Mathematics, Computer Science
- 2019 IEEE International Symposium on Information Theory (ISIT)
- 2019

This paper proves the uniform equicontinuity for all three quantum versions of Rényi information, hence it yields the joint continuity of these quantities in the orders and priors, and establishes the concavity in the region of s ∈ (−1, 0) for both Petz’s and the sandwiched versions. Expand

Quantum Sphere-Packing Bounds With Polynomial Prefactors

- Computer Science, Physics
- IEEE Transactions on Information Theory
- 2019

A finite blocklength sphere-packing bound for classical-quantum channels is established, which significantly improves Dalai’s prefactor from the order of subexponential to polynomial and the gap between the obtained error exponent for constant composition codes and the best known classical random coding exponent vanishes, indicating the sphere- packing bound is almost exact in the high rate regime. Expand

Strong Converse Bounds in Quantum Network Information Theory

- Computer Science
- IEEE Transactions on Information Theory
- 2021

In this paper, we develop the first method for finding strong converse bounds in quantum network information theory. The general scheme relies on a recently obtained result in the field of… Expand

Strong Converse Bounds in Quantum Network Information Theory

- Mathematics, Physics
- 2020 IEEE International Symposium on Information Theory (ISIT)
- 2020

We develop the first method for finding strong converse bounds in quantum network information theory. The general scheme relies on a recently obtained result in the field of non-commutative… Expand

On quantum Rényi entropies: A new generalization and some properties

- Physics, Computer Science
- 2013

This work proposes a new quantum generalization of the family of Renyi entropies that contains the von Neumann entropy, min-entropy, collision entropy, and the max-entropies as special cases, thus encompassing most quantum entropie in use today. Expand

Divergence Radii and the Strong Converse Exponent of Classical-Quantum Channel Coding With Constant Compositions

- Computer Science, Physics
- IEEE Transactions on Information Theory
- 2021

It is shown that the analogous notion of Rényi capacity, defined in terms of the sandwiched quantum Rényu divergences, has the same operational interpretation in the strong converse problem of constant composition classical-quantum channel coding. Expand

Convexity and Operational Interpretation of the Quantum Information Bottleneck Function

- Physics, Computer Science
- 2019 IEEE International Symposium on Information Theory (ISIT)
- 2019

It is shown that the quantum IB function characterizes the rate region of the quantum source coding with quantum side information at the decoder, which has recently been solved by Hsieh and Watanabe, and that the related privacy funnel function is concave. Expand

Non-Asymptotic Classical Data Compression With Quantum Side Information

- Physics, Computer Science
- IEEE Transactions on Information Theory
- 2021

This paper analyzes classical data compression with quantum side information in the so-called large and moderate deviation regimes, and determines the speed of convergence of the error probability to zero and is shown that it is given in terms of the conditional information variance. Expand

Strong Converse Exponent for Classical-Quantum Channel Coding

- Physics, Computer Science
- ArXiv
- 2014

The exact strong converse exponent of classical-quantum channel coding, for every rate above the Holevo capacity, is determined, an exact analogue of Arimoto’s, given as a transform of the Rényi capacities with parameters α>1. Expand

Quantum Rate Distortion, Reverse Shannon Theorems, and Source-Channel Separation

- Mathematics, Physics
- IEEE Transactions on Information Theory
- 2013

This paper proves that the quantum rate-distortion function is given in terms of the regularized entanglement of purification, and establishes several quantum source-channel separation theorems in theEntanglement-assisted setting, in which a necessary and sufficient condition for transmitting a memoryless source over aMemoryless quantum channel up to a given distortion. Expand