Reply to Comment on "Strong Quantum Darwinism and Strong Independence are Equivalent to Spectrum Broadcast Structure"

TL;DR

This paper clarifies a correction to a previous work on quantum Darwinism, emphasizing that the core proofs remain valid despite a mathematical oversight in defining 'strong independence' for Spectrum Broadcast Structure.

Contribution

The authors correct a mathematical expression related to 'strong independence' while confirming that their original qualitative definitions and proofs remain valid.

Findings

Mathematical expression of 'strong independence' was corrected.

Original qualitative definitions and proofs are unaffected.

The core results about Spectrum Broadcast Structure remain valid.

Abstract

In a recent comment [Feller et. al, arXiv:2101.09186] on our Letter [Phys. Rev. Lett. 122, 010403 (2019)], Feller et. al identified a mistake in our mathematical expression of "strong independence" for states that satisfy Spectrum Broadcast Structure. We concede that we wrote a mathematical condition that is necessary but not sufficient. However, we used the original and correct qualitative definition for "strong independence" throughout the paper and in our proofs, therefore the proofs and statements, aside from the aforementioned mathematical expression, remain correct.