A quantum solution to the arrow-of-time dilemma: reply

TL;DR

The paper discusses a quantum approach to the arrow-of-time dilemma, clarifying the role of quantum mutual information and emphasizing the need for a low entropy initial state.

Contribution

It corrects a flaw in the previous argument by emphasizing quantum mutual information and highlights the necessity of a low entropy initial condition.

Findings

Quantum mutual information is the appropriate measure of information.

The core argument remains valid despite the flaw.

A low entropy initial state is necessary for the argument.

Abstract

I acknowledge a flaw in the paper "A quantum solution to the arrow of time dilemma": as pointed out by Jennings and Rudolph, (classical) mutual information is not an appropriate measure of information. This can be traced back to the quantum description underlying my analysis, where quantum mutual information is the appropriate measure of information. The core argument of my paper (summarized in its abstract) is not affected by this flaw. Nonetheless, I point out that such argument may not be adequate to account for all phenomena: it seems necessary to separately postulate a low entropy initial state.