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arXiv:2101.10756

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

Thao P. Le, Alexandra Olaya-Castro

Published Jan 26, 2021• 0 citations
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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.

DOI
10.48550/arxiv.2101.10756

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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.
In a recent Letter [Phys. Rev. Lett. 122, 010403 (2019)], an equivalence is proposed between the so-called Spectrum Broadcast Structure for a system-multienvironment quantum state, and the conjunction of two information-theory notions: (a) Strong Quantum Darwinism; and (b) Strong Independence. Here, we show that the mathematical formulation of condition (b) by the authors (namely, the pairwise independence of the fragments of the environment, conditioned on the system), is necessary but not sufficient to ensure the equivalence. We propose a simple counter-example, together with a strengthened formulation of condition (b), ensuring the equivalence proposed by the authors.