# Relating Entropies of Quantum Channels

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Preliminaries

**Definition**

**1**

**Definition**

**2**

**Lemma**

**1.**

**Proof.**

## 3. Quantum Unital Qubit Channels

**Theorem**

**1.**

**Lemma**

**2.**

**Proof.**

**Lemma**

**3.**

**Proof.**

## 4. Asymptotic Case

**Conjecture**

**1**.

**Theorem**

**2.**

**Proof.**

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The quantity $D(\sigma \parallel \gamma )$ where $\sigma $ and $\gamma $ are as in Equations (37) and (38) respectively. The plots are for $\nu =\mathrm{Dir}(d,1)$ (red), $\nu =\mathrm{Dir}(2,1)$ (blue), $\nu =\mathrm{Dir}(d,2)$ (yellow) and $\nu =\delta (1/d)$ (green). The dashed line is the quantity $log\left(d\right)-\frac{1}{2}$.

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Kurzyk, D.; Pawela, Ł.; Puchała, Z. Relating Entropies of Quantum Channels. *Entropy* **2021**, *23*, 1028.
https://doi.org/10.3390/e23081028

**AMA Style**

Kurzyk D, Pawela Ł, Puchała Z. Relating Entropies of Quantum Channels. *Entropy*. 2021; 23(8):1028.
https://doi.org/10.3390/e23081028

**Chicago/Turabian Style**

Kurzyk, Dariusz, Łukasz Pawela, and Zbigniew Puchała. 2021. "Relating Entropies of Quantum Channels" *Entropy* 23, no. 8: 1028.
https://doi.org/10.3390/e23081028