Comment on "Convergence of macrostates under reproducible processes" [Phys. Lett. A 374: 3715-3717 (2010)]

TL;DR

This paper presents counterexamples disproving the superadditivity of quantum relative entropy for full-ranked states, challenging existing inequalities and proposing a new conjecture on weak superadditivity.

Contribution

It provides the first known counterexamples to superadditivity of quantum relative entropy and introduces a conjecture on weak superadditivity.

Findings

Counterexamples show superadditivity inequality does not hold for full-ranked states

Inequality for quantum channels and complementary channels is invalidated

A new conjecture on weak superadditivity is proposed

Abstract

In this Letter, two counterexamples show that the superadditivity inequality of relative entropy is not true even for the full-ranked quantum states. Thus, an inequality of quantum channels and complementary channels is not also true. Finally, a conjecture of weak superadditivity inequality is presented.