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More examples of additivity violation of the regularized minimum output entropy in the commuting-operator setup

Mehrdad Kalantar, Homayoon Shobeiri

Abstract

We generalize recent results of Collins and Youn (2022), presenting new classes of quantum channels violating the additivity of the regularized minimum output entropy in the commuting-operator setup.

More examples of additivity violation of the regularized minimum output entropy in the commuting-operator setup

Abstract

We generalize recent results of Collins and Youn (2022), presenting new classes of quantum channels violating the additivity of the regularized minimum output entropy in the commuting-operator setup.
Paper Structure (6 sections, 8 theorems, 28 equations)

This paper contains 6 sections, 8 theorems, 28 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Haagerup-type inequalities for direct products
  4. Additivity violation of the regularized MOE
  5. Examples

Key Result

Lemma 1

Let $G$ and $H$ be discrete groups, $p, q>0$, and $E\subset G$, $F\subset H$ are such that $\|\lambda_{_G}(f)\|\, \le\, p \,\|f\|_{_2}$ for all $f\in\mathbb C [G]$ with ${\rm supp}(f)\subseteq E$, and $\|\lambda_H(f')\|\, \le\, q\, \|f'\|_{_2}$ for all $f'\in\mathbb C [H]$ with ${\rm supp}(f')\subse

Theorems & Definitions (17)

  • Lemma 1
  • proof
  • Corollary 2
  • proof
  • Theorem 3
  • proof
  • Lemma 4
  • proof
  • Proposition 5
  • Theorem 6
  • ...and 7 more