Additive invariants on quantum channels and applications to regularized minimum entropy

TL;DR

This paper introduces two additive invariants for quantum channels, providing bounds on the regularized minimum entropy and exploring cases where these invariants equal one.

Contribution

The paper defines new additive invariants for quantum channels and links them to bounds on the regularized minimum entropy, with illustrative examples.

Findings

Invariants can be less than 1, providing positive lower bounds for entropy.

Examples demonstrate cases where invariants are below 1.

Analysis of cases where invariants equal 1.

Abstract

We introduce two additive invariants of output quantum channels. If the value of one these invariants is less than 1 then the logarithm of the inverse of its value is a positive lower bound for the regularized minimum entropy of an output quantum channel. We give a few examples in which one of these invariants is less than 1. We also study the special cases where the above both invariants are equal to 1.