Abstract
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.
Highlights
In their Letter [1], the authors introduce the notions of (a) “strong quantum Darwinism” and (b) “strong independence.” It is proposed that, taken together, conditions (a) and (b) are equivalent to the so-called spectrum broadcast structure (SBS) for the system-environment quantum state ρSE
We propose a stronger condition (b0), ensuring the equivalence of conditions (a) and (b0) with SBS
Open access publication funded by the Max Planck Society
Summary
In their Letter [1], the authors introduce the notions of (a) “strong quantum Darwinism” and (b) “strong independence.” It is proposed that, taken together, conditions (a) and (b) are equivalent to the so-called spectrum broadcast structure (SBS) for the system-environment quantum state ρSE (throughout this Comment, we follow the notations and definitions used in the Letter). We first construct a (completely classical) counterexample of a state with no SBS yet satisfying conditions (a) and (b). We propose a stronger condition (b0), ensuring the equivalence of conditions (a) and (b0) with SBS. Our counterexample is the state (0 ≤ p ≤ 1) With the relative states ρðE0Þ 1⁄4 Π000; ð2Þ
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